A candy factory needs a box that has a volume of 30 cubic inches. The width should be 2 inches less than the height, and the length should be 5 inches greater than the height. What should the dimensions of the box be, in inches? (You may use your graphing calculator to help you with this problem, but be sure to define all variables and show the function used to find the dimensions.)

Q: Find the inflection points of the function f (x) = x3 - 3x2 + 5, and explain why the graph has the…

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Q: /(x) - 4**1 - 2

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Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = (6 −…

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Q: Determine the end behavior of the graph of the function.f (x) = 8x3(4 - x)(7x - 6)4

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Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = 6x4 −…

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Q: The function that has an x-intercept of -2 and a y-intercept of -2/3

A: We can find the function as below

Q: Find the points of inflection and discuss the concavity of the graph of the function.

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Q: The graph of the function f(x) = 3x4 - x3 + 5x2 - 2x - 7 resembles the graph of ________ for large…

A: The graph of the function f(x) = 3x4 - x3 + 5x2 - 2x - 7resembles the graph of ________ for large…

Q: Graph the the quadratic function f(x) = 5 - (x + 2)2. Give the function domain and range.

A: Given  The quadratic function is  f(x) = 5 - (x + 2)2  . The vertex form of the quadratic equation…

Q: Determine whether the function is one-to-one.(a) y = 4x2 + 3(b) y = 2x + 3 - 5

A: Our Aim is to determine whether the function given below is one-to-one or not?(a)…

Q: Determine where the graph of the function f(x) = 2x3 - 6x is concave up and where it is concave down

A: Known fact: The graph of the function fx is concave up on I if f''x>0 for all x in I. The graph…

Q: Determine the maxima and minima of the function: y=2+12x-x^3

A: If second derivative is less than zero then maxima and if greater than zero then minima

Q: Why should the definitions of increasing and decreasing functions must be satisfied by every pair of…

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Q: Graph the function. 2) f(x) = X + 2)(x + 5) x2 - 36

A: We have to graph the function

Q: Write the function whose graph is the graph of y = x3 , but is: Horizontally stretched by a factor…

A: Write the function whose graph is the graph of y = x3 , but is: Horizontally stretched by a factor…

Q: y=x^2, but is vertically stretched by a factor of 6.

A: Vertically stretching a parabolic function implies that the stretching factor should be greater than…

Q: Describe the end behavior of the graph of the function f(x)=5(4)x−4.

A: The given function is fx=54x-4=20x-4. It is a linear function which is part from the family of…

Q: The graph of f(x)=3x is reflected about the y-axis and stretched vertically by a factor of 4 . What…

A: Given,         The graph of f(x)=3x is reflected about the y-axis and stretched vertically by a…

Q: Determine the points in which the function shifts from increasing to decreasing and vice- versa.…

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Q: Complete the equation for the piecewise function graphed below. 6+ -7 -6 -4 -3 -2 -I -3 -4- -6- { if…

A: Equation of straight line passing through (xo , yo) with slope m is given by,              Y - yo…

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Consider the function, fx=x-23x-1 To calculate the double derivatives of the given function,…

Q: determine where the graph of the function is concave upward and where it is concave downward. g(x)=…

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Q: Find the maximum value of the function below. f(x) = -1 - 2x - 2x2

A: Given : fx = -1-2x-2x2

Q: Write the function whose graph is the graph of y=x3 but is reflected across the x axis

A: The graph of y=x3 is as shown below:

Q: graph the functions. f (x) = |x| + 4

A: The graph of a function is drawn by plotting the points x, f(x) for different values of x and then…

Q: Graph the function. 3x 40) f(x) = (x + 5)(x - 3)

A: For the given graph  find vertical asymptotes , horizontal asymptotes and intercepts  and graph it.

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Differentiate the function f(x)=-x3+6x2-5 with respect to x two times and carry out algebraic…

Q: write the function whose graph is the graph of y = x3, but     Vertically stretched by a factor of 4

A: A function can be obtained from a parent function by transformations like stretching vertically,…

Q: A shipping crate has a square base with sides of length x feet, and it is half as tall as it is…

A: Square base, with sides of length x feet, and it is half as tall as its wide.

Q: Determine whether the following statement is true or false, and explain why. The function ƒ(x) = x2…

A: The given function is f(x)=x2-6x+4

Q: How can you tell from the equation g(x)=8(1/2)^x that the graph of the function decreases

A: Given function is  g(x)=8(1/2)x

Q: True or False The y-intercept of the graph of the functiony = f9x), whose domain is all real…

A: The intercepts are the points where the graph of the function crosses the axes.  When the graph of…

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = 2 − 7x4

A: Consider the given function fx=2-7x4

Q: write the function whose graph is the graph  of y=x2 but os horizontally stretched by a factor of 3

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Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = 4 − x −…

A: Consider the function  fx = 4 − x − 3x4

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = x3 −…

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Q: Write the function whose graph is the graph of y = x3 , but is: Reflected about the x-axis

A: Given, y=x3 if we take reflection then all values of y are reflected from above the x-axis to below…

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x)=6x4-x2

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Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = x√(9 −…

A: The function is given as x9−x In order to find the inflection point and concavity, second derivative…

Q: The publisher of a medical newsletter estimates that with x thousand subscribers its monthly revenue…

A: Given that the publisher of a medical newsletter estimates that with x thousand subscribers its…

Q: What is the x - intercept of the function whose graph appears below: 3 2 -3 -2 2 3 -2 -4

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Q: Give the slope and y-intercept for the graph of the function f(x) = 16 – 5(2 – 5x). %3D

A: Given,             The function is fx=16-52-5x.We know that,            The equation of the line in…

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x ^ 2 - 9…

A: Given function fx=x2-9 The given point is (0,-1) ,To find the closest point on the graph First…

Q: Your cell phone carrier is offering you a new iPhone 12 for $800 with a $60 monthly plan.  The total…

A: We are given with the total cost for the iPhone and we are also given with the average monthly cost…

Q: Proble Diego wrote f(x) = (x + 2)(x – 4) as an example of a function whose graph has x-intercepts at…

A: Here x intercept comest at x=4,-2.

Q: Find the point of inflection of the graph of the function. f(x) = 2 – 7x4

A: Consider the given function y=fx=2-7x4 First, find the first derivative of the function…

Q: Is the function h(x)=-|x-4| +3 a one -one function?

A: This is an absolute value function , so for two values of x we will find same value of y.

Q: Why must a cubic function have at least one x-intercept

A: A cubic function with REAL coefficients can have either one x-intercept or 3 x-intercepts. This is…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.