Consider the function: F(x) = x^3 – 3x2 + 6
(a) (10 points) Find the critical value(s) (b) (5 points) On what intervals is the function increasing and decreasing? (c) (5 points) Find the location (x-values) of the local min and max. Please clearly label your answers.
Answers
The location of the local max is x = 0 and the location of the local min is x = 2.
(a) To find the critical value(s), we need to take the derivative of the function and set it equal to zero:
F'(x) = 3x^2 - 6x
3x(x - 2) = 0
x = 0 or x = 2
So the critical values are x = 0 and x = 2.
(b) To determine where the function is increasing and decreasing, we need to look at the sign of the derivative. When F'(x) > 0, the function is increasing, and when F'(x) < 0, the function is decreasing. From part (a), we know that the critical values are x = 0 and x = 2, so we can use those to create intervals and test the sign of F'(x) in each interval:
Interval (-∞, 0): F'(-1) = 9 > 0, so F(x) is increasing on this interval.
Interval (0, 2): F'(1) = -3 < 0, so F(x) is decreasing on this interval.
Interval (2, ∞): F'(3) = 27 > 0, so F(x) is increasing on this interval.
Therefore, F(x) is increasing on (-∞, 0) and (2, ∞) and decreasing on (0, 2).
(c) To find the location of the local min and max, we need to look for the points where the derivative changes sign. Since we already found the critical values in part (a), we just need to check the sign of F'(x) near those values:
Near x = 0: F'(-0.5) = 2.25 > 0 and F'(0.5) = -2.25 < 0, so there is a local max at x = 0.
Near x = 2: F'(1.5) = -1.125 < 0 and F'(2.5) = 13.125 > 0, so there is a local min at x = 2.
Therefore, the location of the local max is x = 0 and the location of the local min is x = 2.
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Related Questions
Pleas answer it now in two minutes
Answers
Answer:
30
Step-by-step explanation:
cos^-1(square root of 3 divided by 2)
Question 1 (1 point) Home Remodelers, Inc., and Imogen enter into a contract for a sale of cabinets and countertops. Home Remodelers merchant who deals in goods of the kind sold, notes that its goods come with an implied Under the UCC, this means that the goods are reasonably warranty of merchantabilit fit for the buyer's particular purpose. O fit for the ordinary purpose for which such goods are used. O suitable for resale at an acceptable price. C the best quality that money can buy Save Question 2 (1 point) Olive, an agent for Precision Paving Corporation, enters into an unauthorized contract with Quality Asphalt, Inc.
Answers
The answer provided illustrates the concept of implied and express warranties, unilateral and bilateral contracts, voidable and void contracts, and executory consideration. It also provides number of examples of each of these concepts.
1. O fit for the ordinary purpose for which such goods are used.
2. A enforce the contract against Olive.
3. C An express warranty must be in writing and signed by the parties.
4. C supported by consideration.
5. O is void.
6. C enforceable.
7. O is a rejection and counteroffer.
8. O A promise to do something in the present in exchange for something else in the future.
9. A An offer to pay a reward for the return of lost property.
10. C An offer to do something in the future in exchange for something else in the present.
The answer provided illustrates the concept of implied and express warranties, unilateral and bilateral contracts, voidable and void contracts, and executory consideration. It also provides number of examples of each of these concepts.
The complete question is :
Question 1 (1 point) Home Remodelers, Inc., and Imogen enter into a contract for a sale of cabinets and countertops. Home Remodelers merchant who deals in goods of the kind sold, notes that its goods come with an implied Under the UCC, this means that the goods are reasonably warranty of merchantabilit fit for the buyer's particular purpose. O fit for the ordinary purpose for which such goods are used. O suitable for resale at an acceptable price. C the best quality that money can buy Save Question 2 (1 point) Olive, an agent for Precision Paving Corporation, enters into an unauthorized contract with Quality Asphalt, Inc. Quality Asphalt may, at its option, A enforce the contract against Olive. O enforce the contract against Precision Paving. C void the contract. Save Question 3 (1 point) Which of the following statements about an express warranty is true? A An express warranty does not need to be in writing. O An express warranty does not need to be signed by the parties. C An express warranty must be in writing and signed by the parties. Save Question 4 (1 point) In order to be enforceable, a contract must be A fair and equitable to both parties. O signed by both parties. C supported by consideration. Save Question 5 (1 point) A contract that is void because of a mistake by one of the parties O is voidable. A is void. C is still enforceable. Save Question 6 (1 point) A contract between two individuals is generally A voidable. O void. C enforceable. Save Question 7 (1 point) Phil makes an offer to sell a house to Sally for $200,000. Sally responds by saying that she will buy the house for $200,000, but wants to add a condition that the house must pass an inspection. This response A is an acceptance of the offer. O is a rejection and counteroffer. C is a condition of acceptance. Save Question 8 (1 point) Which of the following is an example of Executory consideration? A A promise to do something in the future in exchange for something else in the present. O A promise to do something in the present in exchange for something else in the future. C A promise to do something in the future in exchange for something else in the future. Save Question 9 (1 point) Which of the following is an example of a unilateral contract? A An offer to pay a reward for the return of lost property. O An offer to do something in the present in exchange for something else in the future. C An offer to do something in the future in exchange for something else in the present. Save Question 10 (1 point) Which of the following is an example of an implied contract? A An offer to pay a reward for the return of lost property. O An offer to do something in the present in exchange for something else in the future. C An offer to do something in the future in exchange for something else in the present. Save
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What was Earth's air composed of during the Cretaceous Period
Answers
During the Cretaceous Period, Earth's air composition was similar to the present-day composition, consisting primarily of nitrogen (N2) and oxygen (O2).
The atmosphere contained approximately 78% nitrogen and 21% oxygen, with trace amounts of other gases such as carbon dioxide (CO2), water vapor (H2O), and noble gases.
However, the precise levels of these gases varied over time due to natural processes and geological events. The Cretaceous Period, which lasted from approximately 145 million to 66 million years ago, was characterized by high global temperatures and a lush environment, supporting a diverse range of plant and animal life.
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PLEASE HELP
Describe the behavior of the graph below.
A downward parabolic graph in X-Y coordinate.
A.
The graph is increasing for all values of x.
B.
The graph is decreasing when x > 0.
C.
The graph is increasing when x > 0.
D.
The graph is decreasing when x < 0.
Answers
The correct answer is D. The graph is a downward parabola, which means it opens downwards and is decreasing. This occurs for all negative values of x, and is also decreasing for values of x close to zero.
What is Graph?A graph is a visual representation of data or information, typically shown using lines, bars, dots, or other symbols to illustrate relationships, trends, and patterns.
What is parabola?A parabola is a U-shaped curve that is symmetric and can be represented by a quadratic equation. It is a type of conic section and appears in many areas of mathematics and physics.
According to the given information:
The correct answer is D. The graph is a downward parabola, which means that it opens downwards and has a maximum point at the vertex. The vertex is located at x = 0, and since the graph is decreasing on both sides of the vertex, it means that it is decreasing when x < 0. As x approaches negative infinity, the graph becomes more and more steep, and as x approaches positive infinity, the graph becomes flatter and flatter. This behavior is typical of a quadratic function with a negative leading coefficient. In this case, the graph represents a situation where the dependent variable decreases as the independent variable increases up to a certain point, after which it starts increasing again.
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the quantity 2.67 × 103 m/s has how many significant figures?
Answers
The quantity 2.67 × 10³ m/s has three significant figures because the digits 2, 6, and 7 are all significant, and the exponent 3, which represents the power of 10, is not considered a significant figure.
Scientists use significant figures to indicate the level of accuracy and precision of a measurement. The significant figures are the reliable digits that are known with certainty, plus one uncertain digit that has been estimated or measured with some degree of uncertainty. In determining the significant figures of a number, the following rules are applied: All non-zero digits are significant.
For example, the number 345 has three significant figures. Zeroes that are in between two significant figures are significant. For example, the number 5004 has four significant figures. Zeroes that are at the beginning of a number are not significant. For example, the number 0.0034 has two significant figures. Zeroes that are at the end of a number and to the right of a decimal point are significant. For example, the number 10.00 has four significant figures.
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When multiplying two variables, how is using the
Distributive Property similar to using a table?
Answers
Newton's third law states that if object A exerts a force on object B, object B must respond with a force of equal size and in the opposite direction. This law reflects nature's symmetry: forces always exist in pairs, and one body cannot exert a force on another without experiencing one.
The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2. 3(10 + 2) = ? According to this property, you can add the numbers and then multiply by 3.
Hardest question in the world!
If solved huge surprise
Once upon a time, an old lady want to sell her eggs at the local market.
When asked how many she had she replied I can’t count past 100 but I know that:
If you divide the number of eggs by two there will be one egg left.
If you divide the number of eggs by three there will be one egg left.
If you divide the number of eggs by four there will be one egg left.
If you divide the number of eggs by five that will be one egg left.
If you divide the number of eggs by six there will be one eggs left.
If you divide the number of eggs by someone there will be one egg left.
If you divide the number of eggs by eight there will be one egg left.
If you divide the number of eggs by nine there will be one egg left.
If you divide the number of eggs by 10 that will be one egg left.
If you divide the number of eggs by 11 that will be no eggs left
how many eggs did the Lady have
Answers
9514 1404 393
Answer:
25201
Step-by-step explanation:
The number of eggs is one more than some factor times the LCM of 2, 3, 4, 5, 6, 7, 8, 9, and 10. That factor will make the result be a multiple of 11. Since the LCM is 2520, and that has a remainder of 1 modulo 11, we know we must multiply it by 10 before adding 1 in order to get a multiple of 11.
That is, the lady has 2520×10 +1 = 25201 eggs.
Write a polynomial function with rational coefficients so that P(x)=0 p open x close equals 0 has the given roots.
7 and 12
Answers
Answer:
p(x)=x^2 -17 x + 84
Step-by-step explanation:
p(x)=(x-7)(x-12)
= x^2-17x+84
Find the measure of angle x.
A.24
B.27
C.63
D.65
Answers
What is the volume of a cylinder, in cubic cm, with a height of 19cm and a base diameter of 6cm? Round to the nearest tenths place
Answers
Answer:
volume of a cylinder = 536.9 cm³
Step-by-step explanation:
volume of a cylinder, V = πr²h
where π = 3.14
h = 19 cm
r = ?
given is diameter = 6 cm
as we know, r = d/2 = 6/2 = 3 cm
by substituting the values in the formula,
V = 3.14 * 3² * 19
= 536.94 cm³
by rounding off to the nearest tenth place,
volume of a cylinder = 536.9 cm³
Answer:
v = 537.2 cm3
Step-by-step explanation:
volume:
\(v=\pi r^{2} h\)
\(r=d/2=6/2=3cm\)
\(h=19cm\)
\(v=\pi (3)^{2} (19)=171\pi\)
\(v=537.21\)
Rounded nearest tenth:
\(v=537.2cm^{3}\)
Hope this helps
How many different numbers can be obtained using five binary bits? A)64 B)32 C)31 D)63.
Answers
In binary representation, each bit can be either 0 or 1. Using five binary bits, we can obtain 32 different numbers. Therefore, the correct answer is (B).
With five binary bits, we have five positions, and each position can have two possibilities (0 or 1). To calculate the total number of different numbers we can obtain, we need to raise 2 to the power of the number of bits. In this case, we have \(2^5,\) which equals 32. Therefore, we can obtain 32 different numbers using five binary bits. To understand this concept, we can think of each binary bit as a switch that can be either on (1) or off (0). With five switches, we have a total of 32 different combinations or numbers that can be represented. These numbers range from 0 (all switches off) to 31 (all switches on). Therefore, the correct answer is (B), which states that we can obtain 32 different numbers using five binary bits.
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Which are irrational and which are rational ?
Answers
Answer: 8/9 is rational
.2593 irrational
square root of 7: irrational
square root of .25 is rational
square root of 14: irrational
0 is a: rational
square root of 280: irrational
square root of 35: is irrational
.2222: is rational
square root of 3r is a rational number......
Step-by-step explanation:
what is a polygon with all sides and angles congruent
Answers
A regular polygon is a polygon with all sides and angles congruent. It exhibits symmetry and uniformity in its sides and angles, creating a visually appealing shape.
A polygon with all sides and angles congruent is called a regular polygon. In a regular polygon, all sides have the same length, and all angles have the same measure. This uniformity in the lengths and angles of the polygon's sides and angles gives it a symmetrical and balanced appearance.
Regular polygons are named based on the number of sides they have. Some common examples include the equilateral triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), and so on. The names of regular polygons are derived from Greek or Latin numerical prefixes.
In a regular polygon, each interior angle has the same measure, which can be calculated using the formula:
Interior angle measure = (n-2) * 180 / n
Where n represents the number of sides of the polygon.
The sum of the interior angles of any polygon is given by the formula:
Sum of interior angles = (n-2) * 180 degrees
Regular polygons have several interesting properties. For instance, the
exterior angles of a regular polygon sum up to 360 degrees, and the measure of each exterior angle can be calculated by dividing 360 degrees by the number of sides.
Regular polygons often possess symmetrical properties and are aesthetically pleasing. They are commonly used in design, architecture, and various mathematical applications.
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a rectangle is to be inscribed in a semicircle of radius 2. what is the largest area the rectangle can have, and what are its dimensions.
Answers
The largest area a rectangle can have when inscribed in a semicircle of radius 2 is 4 square units.
The dimensions of this rectangle are 2 units by 2 units. This occurs when the sides of the rectangle are parallel to the diameter of the semicircle, so that each vertex of the rectangle lies on the circumference of the semicircle.
The length of the rectangle is equal to the diameter of the semicircle, or 2 units, and its width is half the diameter, or 2/2 = 1 unit. The area of this rectangle is equal to the length times the width, or 2 * 1 = 2 square units.
Since the rectangle is inscribed in a semicircle, its dimensions must be equal, so the largest area rectangle that can be inscribed in a semicircle of radius 2 has sides of length 2 units and an area of 4 square units.
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If the assumptions for the large sample confidence interval for the population proportion are not met what adjustments can be made? OUse phat (X+1)/(N+3) insteac. Add enough successes to make there be 195 O Add enough successes to make there be 15 successes and 15 failures. Use phat = (X+2)/(N+4) instead. Nothing can be done.
Answers
If the assumptions for the large sample confidence interval for the population proportion are not met, adjustments can be made is-
D) Nothing can be done.
If the assumptions for the large sample confidence interval for the population proportion are not met, adjustments can be made to improve the accuracy of the confidence interval calculation.
In this case, there are three potential adjustments mentioned:
A) Use phat (X+1)/(N+3) instead.
B) Add enough successes to make there be 15 successes and 15 failures.
C) Use phat = (X+2)/(N+4) instead.
These adjustments are made to address the limitations or violations of assumptions. Let's discuss each option:
A) Use phat (X+1)/(N+3) instead:
This adjustment incorporates an adjustment factor to the usual formula for the sample proportion (phat). By adding 1 to both the numerator (number of successes) and the denominator (sample size), it attempts to mitigate potential issues related to extreme values.
B) Add enough successes to make there be 15 successes and 15 failures:
This adjustment involves artificially modifying the data to ensure a balanced number of successes and failures. By doing so, it aims to satisfy the assumption of a sufficiently large sample size and approximate a normal distribution. However, it should be noted that altering the data in this manner may introduce biases and may not be statistically appropriate in certain cases.
C) Use phat = (X+2)/(N+4) instead:
Similar to option A, this adjustment adds a correction factor to the usual formula for the sample proportion. By adding 2 to both the numerator and denominator, it aims to address potential issues associated with small sample sizes or extreme values.
D) Nothing can be done:
This option suggests that no adjustments can be made when the assumptions for the large sample confidence interval for the population proportion are not met.
Therefore, if the assumptions for the large sample confidence interval for the population proportion are not met, adjustments can be made is-
D) Nothing can be done.
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It takes Anastasia 45 minutes to walk 2 miles to the park At this rate, how
many minutes should it take her to walk 3 miles?
Answers
Answer:
54 minutes
Step-by-step explanation:
45 minutes per 2.5 miles
45/2.5 = 18 minutes per mile
3 miles * 18 minutes = 54 minutes
If a line passes through (6,4) and (12,7), what is the slope? I really need help and if you can please explain how you got the asnwer
Answers
Answer:
0.5 OR 1/2
Step-by-step explanation:
Since the two points are (6,4) and (12,7) you would find the distance in x and y.
Slope = change in y/ change in x
Change in y: the y coordinates are 4 and 7, so 4 + 3 = 7. +3 is the change.
Change in x: the x coordinates are 6 and 12, so 6 + 6 = 12. +6 is the change.
Slope = 3/6 = 1/2 = 0.5 = 50%
Hope this helps :D
Help me out please????
Answers
Answer:
fromfromfromfromfromfromfromfromfromfromfromfromfromfromfromfromfrom
Step-by-step explanation:
Camilla took a $23,500 secured auto loan that
allows her to make no payments for 18
months. If interest is still compounded
monthly at a rate of 6.3%, what will her
balance be in 18 months when she starts
making payments?
Answers
What would be an appropriate measure to describe the amount of water in a puddle?
milliliters
miles
tons
feet
Answers
Answer:
Mililiters
Step-by-step explanation:
Since a puddle is an extremely small body of water you should use the smallest measurement
PLEASE HELP I WILL GIVE YOU POINTS,BRAINLIEST, AND A COOKIE !!
Answers
Answer:
20 maybe
Step-by-step explanation:
Answer:
20 because you have to cross multiple
Consider following autonomous system:x ′ =y−2y ′ =(x+1)(x−2) (a) Graph the nullclines of the system and locate all equilibrium points. (b) Draw arrows along the nullclines. (c) Sketch an arrow in each open region divided by the nullclines that suggests the direction in which a solution point is moving when it is in that region.
Answers
The equilibrium points are y = 2 , x = -1 , 2
Equilibrium is a state in which opposing forces or influences are balanced. It is a state of rest or balance resulting from the equal action of opposing forces. In economics, equilibrium is a situation in which the forces of supply and demand in a market are balanced and there is no tendency for the price to either rise or fall.
The given system is
x' = y − 2
y' = (x+1)(x-2)
a) The equilibrium points are given by
f(x) = 0 and g(x) = 0
y - 2 = 0 and (x + 1)(x - 2) = 0
y = 2 and x = -1 , 2
So the equilibrium points are (-1,2) and (2,2)
The x null clines are given by x' = 0
y - 2 = 0
y = 2
The y null clines are given by y' = 0
(x + 1)(x - 2) = 0
(x + 1) = 0 or (x - 2) = 0
x = -1 or x = 2
So the graph is given below
In the given figure 1.1
The dotted lines are the nullclines.
b)The nullclines with the arrow are given below:
In the given figure 1.2
c) The arrows in the open region is given below:
In the given figure 1.3
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The complete question is:
Consider following autonomous system : x ′ =y−2, y ′ =(x+1)(x−2)
(a) Graph the nullclines of the system and locate all equilibrium points.
(b) Draw arrows along the nullclines.
(c) Sketch an arrow in each open region divided by the nullclines that suggests the direction in which a solution point is moving when it is in that region.
winch one is biger
4/9 0r 1/12
Answers
Answer:
4/9
Step-by-step explanation:
I did the butterfly method to see which one is the bigger one
Answer:
4/9
Step-by-step explanation:
The value of Royce Company's computer equipment
is decreasing in value by 13% each year. If they are
currently worth 1.5 million dollars, write an
exponential function to estimate the company's value
after x years.
A. y = 1.5(0.13)^x
B. y = 1.5(0.87)^x
C. y = 0.87(1.5)^x
D. y = 0.87x + 1.5
Answers
PLEASE HELP IM GOING TO GET IN SO MUCH TROUBLE
Freshman and sophomores were surveyed during lunch about their favorite professional football team.
A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent. The second bar is labeled Dolphins, with freshman from 0 to 45 percent and sophomores from 45 to 100 percent, and the third bar is labeled Buccaneers, with freshmen from 0 to 45 percent and sophomores from 45 to 100 percent.
If 140 students selected Jaguars, how many of those students are freshman?
56 students
63 students
77 students
84 students
Answers
Answer:
63 students.Step-by-step explanation:
if it helps, pls like and commentsAnswer:
63 students
Step-by-step explanation:
8( 7 + 9) = 8(7) + 8(9)which property is this?
Answers
The given equation is
\(8(7+9)=8(7)+8(9)\)We multiply 8 by each term in the bracket on the right side
Then we used the distributive property
The answer is D
I need help figuring out This problem .
Answers
The value of x in the two congruent triangles is 3.9 and length CB is 53.9.
What is the value of x in the given triangle?The value of x can be determined by applying the principle of congruent theorem.
The congruent theorem states that, if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.
( 11x + 11 ) / 77 = 21 / 30
11x + 11 = 53.9
11x = 53.9 - 11
11x = 42.9
x = 42.9 / 11
x = 3.9 units
The length of CB = ( 11 x 3.9 ) + 11 = 53.9
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Which function shows the parent function, f(x) = x^2, vertically stretched by 4, horizontally shifted right 2, and vertically shifted down 1?
O 4(x+2)^2-1
O 4(x-2)^2-1
O 1/4(x+2)+1
O 1/4(x-2)^2-1
Whoever answers correctly will get Brainliest!!!
Answers
The correct graph of the polynomial is \(4(x-2)^2-1\)
The given parent function is \(f(x) = x^2\)
This means that the graph would be a parabola
because the highest degree is 2
And the graph of \(4(x-2)^2-1\)
is 2 units to the right and 1 unit vertically down
And vertically stretched by 4 units
we know that the graph of f (x) = x^2 is a parabolic graph and is drawn in the first and the second quadrant
Thus the graph of the this equation is also drawn similarly :
the graph is shown below :
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Melissa's yoga class last 46 minutes if the class ended at 6:32 PM what time did the yoga class start
Answers
Answer:
5:46pm
Step-by-step explanation:
6:32 - :46 =
6:00 = :46 - :32 = :14
6:00 = 5:60
5:60 - :14 = :60 - :14 = :46
5:46
Write .00078 in scientific notation
Answers
Answer:
10^-4×7.8
Step-by-step explanation:
7.8×0.0001