A graphing calculator is recommended. A cardboard box has a square base, with each edge of the base having length x inches, as shown in the figure. The total length of all 12 edges of the box is 144 in. (a) Express the volume V of the box as a function of x. V(x) = (b) What is the domain of V? (Use the fact that length and volume must be positive. Enter your answer using interval notation.) (c) Draw a graph of the function V. V V 2000 2000 1500 1500 1000 1000 500 500 10 15 20 10 15 20

Q: find the points of inflection and discuss theconcavity of the graph of the function. f(x)=x…

A: To find: The point of inflection and discuss the concavity of the graph of the function. Given: The…

Q: 1. Sketch the graph of the function: 2x2+ f(x) = 3x-5

A: To sketch the graph of the given function.

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

A: Given, f(x)=6-xx

Q: find the points of inflection and discuss theconcavity of the graph of the function. f(x)=4-x-3…

A: Here the given function is  f(x)=4-x-3x4 differentiate with respect to x

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

A:

Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: From a 18 cm by 18 cm piece of cardboard, square corners are cut so that the sides can be folded up…

Q: length

A: Given: Length of rectangle = 19 cm The perimeter of rectangle = P cm Let the breadth of the…

Q: Find the domain and sketch the graph of the function.   f(x) = |2x+1 |

A: The given modulus function is well defined for all real numbers. Therefore, The domain of given…

Q: Q1// Graph and discuss, with detail, the continuity of the function -1 <x< 0 x2- 1 2x 0 <x< 1 y =…

A: The given function is y=fx=x2-1,-1≤x&lt;02x,0&lt;x&lt;11,x=1-2x+4,1&lt;x&lt;20,2&lt;x&lt;3

Q: Consider the function below. f(x) = √64-x² What is the Domain? What is the Range? Enter your answer…

A: Domain of  64-x2 :We must have 64-x2≥0So,  Solution:  -8≤ x≤ 8  Interval Notation: -8, 8

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

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Q: 8. O f(x) = 3x° – 5x³ + 1

A:

Q: For Exercise, use a graphing utility to graph the piecewise-defined function. for x < -1 (-2.7x –…

A: We are going to plug the piecewise function in a graphing utility as three separate functions

Q: Use a graphing utility to approximate to two decimal places any relative minima or maxima of the…

A: Consider the function  f(x)=-x2+3x-2 Using a graphing calculator, the graph of the above function…

Q: From a 24-cm by 24-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: in this first we will find side of the box and then  Volume of the box = length × breath× height

Q: Find the points of inflection and discuss the concavity of the graph of the function. g(x) = x√(x +…

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Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: Solution is provided below

Q: The area of a rectangle is given by the function A(x) = 3x³ + 6x² + 4x + 8. If the length is defined…

A:

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: 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: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: To find the volume of a box obtained by cutting squares so that the sides fold up to a box. Then…

Q: Sketch the graphs of the functions. 7. f(x) = (x + 2) – 1

A: 7. We have to sketch the graph of fx=x+23-1. Steps: First we will draw the graph for x3. Now to draw…

Q: From a 27-cm by 27-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A:

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

A: solution is given below:

Q: Find the domain and sketch the graph of the function.   f(x) = x2 - 2x + 1

A: Let us consider the given function. Since, the functionis a polynomial, so the domain is all real…

Q: In the function:  f(x)= (9x^2)/ ((x^2)-49) Indicate the domain and range in interval notation.  What…

A: Denominator of the function can not be equal to 0.

Q: Find the domain of the function in interval notation  g(x)= x/ x^2-49

A: We need to find out the domain of the function given.

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

A:

Q: Find the description and graph for the function k (x) = (x + 2)° – 3

A: Given: If the function x3 shifted 2 units left and shifted down by 3 units, we get the function…

Q: List the x-values in the graph at which the function is not differentiable. 2 3. x = 0, x = 3 X = 3…

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Q: An open-top box with a square base is to be constructed by taking a 36 by 36 square piece of…

A: The dimension of the square base is 36 by 36. Since a square of side length x in is cut out from…

Q: Examine the graph of the function f(x) 10x+3x-12r. %3D

A: Given f(x)=10x3+3x2-12x

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: Consider the graph of the functions f(x)=(x−5)² and g(x)=−3x+13. What are the points at which…

A:

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

A:

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: Sketch the graph of the function: (plot at least 4 points on the graph) -5x +2 ,x<0 F(x) = 1-x²-2 x…

A:

Q: Find the domain and sketch the graph of the function.

A: To find the domain and to sketch the graph of the function fx=3-12x   if x≤22x-5   if x&gt;2

Q: What is the domain of h(x) = e 3x + 1? %3D (Type your answer in interval notation.) What is the…

A: Domain : where function defined

Q: What is the zeros, y-intercept, vertex, and axis of symmetry of f(x)=-2x^2-5x+3.  What does a graph…

A:

Q: From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: Please refer the attached image for complete solution.

Q: Sketch the graph of the function f(x) = x³ – 2x² – 5x + 6 using calculus – based analysis. -

A: Given problem:- Sketch the graph of the function f(x) = x3 – 2x2 − 5x + - 6 using calculus - based…

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

A: Our Aim is to find the points of inflection and discuss the concavity of the graph of the function…

Q: Consider the function f(x)=2x^2−2 for x≥0. What is the domain of f−1(x)?  answer in interval…

A: Domain set of all input values where f defined Range set of all output values

Q: Find the x- and y-intercepts of the graph of the function f(x)=−2|x+5|+2.

A: The graph of the function is

Q: Given the function f(x) = -x² +6x+2, discuss its relative maximum and minimum points, the intervals…

A:

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

A: Given, y=x9-x derivate both side  f'(x)=9-x+x29-x9-xf'(x)=18-x29-x3/2

Q: You want to build a pen for your new puppy, and you want to put it next to your barn. You have 200…

A: Draw the diagram of the pen for the puppy.