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.)

Q: 5. What is the domain of the function h(x)= 11 X x 2 1 ?

A:

Q: Sketch the graph of the function defined by the formula 0 , x<-1 f(x) = |1– x² ,-1<x <1 x 2 1

A: Given:     To determine: the graph of f(x)

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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…

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A: The given function is fx=x30-x2. Find the first derivative of fx=x30-x2.…

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A: Given the perimeter (or) Total length of fencing is 1000 ftFrom the given figure total length of…

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A: Given  f(x)=8x3 +81x2−42x−8 on [−8,2].

Q: Find all points of intersection between the graphs of the functions f(x) = (x + 5)(x-4) and g(x) = x…

A: Explanation of the answer is as follows

Q: Find the domain of the function f(x) = /2x – 3 - In interval form, the domain of f is

A: here function is given in form of square root this can't be negative so the value inside is positive…

Q: An open box is to be made from a square piece of cardboard of side 12 inches by cutting out squares…

A: To find the size of squares cut out of the box for maximum volume.

Q: Consider the function f(x) = 2x² – 2 for x > 0. %3D What is the domain of f-(x)? Write your answer…

A: The given function is the one-one function in the given domain.   Replace f(x) by y and then…

Q: The absolute maximum of the function f(x) = 3x² + 3x + 14 over [1, 7]. 182

A: We have to find absolute maxima of the given function   the function is  3x2+3x+14   Over the…

Q: -22- 14

A:

Q: Does the function f(x)=2^x approach a certain real number as the value of x increasing positively?…

A: f(x) = 2x clearly, 2x+1 = 27.2 &gt; 2x  f(x+1) &gt; f(x) or if a E R (i.e. a&gt;0) then f(x+a) = 2x.…

Q: The area of the region between the x-axis and the graph of the f(x) = x3 – x² – 2x,-1 < x < 2 is :

A:

Q: Find the domain of the function written in interval notation. f(x)= square root of x-4 divided by…

A:

Q: g(x) = v2 – 3x %3D

A:

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

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A:

Q: Find the open intervals where f is increasing or decreasing.ƒ(x) = x4 + 4x + 1

A: Given: f(x)=x4+4x+1

Q: Consider f (x) =x³ – 6x²+9x +3 defined on the closed interval .At which value of x does the absolute…

A:

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: Consider the function 3 2 f(x) = 2x + 18x – 162x + 3, - 9 < x < 4. This function has an absolute…

A: Given, f(x)= 2x³+18x²-162x+3 -9=&lt;x=&lt;4

Q: Sketch the graph of the function defined by the formula 0, x<-1 f(x) = /1- x² ,-1< x < 1 x 2 1

A: Given function, f(x)=         0  ,           x≤-11-x2 ,      -1&lt;x&lt;1        x  ,           x≥1

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

Q: 21. Find the "natural" domain of the function f(x)= 4x-10x+4

A:

Q: A wire of length 8x is bent into the shape of a circle. A. Express the circumference of the circle…

A:

Q: Find the open intervals where f is increasing or decreasing.ƒ(x) = x2 + 9x + 8

A: Function calculator: f(x)=x2+9x+8 To get maxima and minima we get f'(x)=0

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A:

Q: Find the domain of the function using interval notation.   f(x)=−2x(x−3)(x−5)

A: Since f(x) = -2x(x-3)(x-5)  is a cubic polynomial. And we know that the domain of all polynomial…

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A:

Q: Determine the number of possible positive and negative zeros for the given function in accordance…

A: To determine the number of possible positive and negative zeros of the function.

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A: Area of the rectangle = 16 m2 The length of one of its sides = x m P = ?

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

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A: Given  f(x)=(3-x)(4+3x)

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A: The root of the equation is 0.755 Also it is evident that it is lying between 0 and 1

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A: Let the figure of the fencing be:

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A:

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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…

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A: Answer : Maximum area should be 4.225 unit2 .

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A:

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

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Q: 1) Analyze and sketch the function f(x) = -x* - 2x + 5x2 %3D

A:

Q: A builder uses the function g defined by g(2) = 80x + 10000 to estimate the cost g(x), in dollars,…

A: Given:- A builder uses the function g defined by g(x) = 80x+10000 to estimate the cost g(x), in…

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Q: Find the absolute extrema of f(x) = 2x³ – 21x² + 72x on the closed interval [0, 5].

A: