W W W The length of the box, as a function of x, is l = The width of the box, as a function of x, is w The volume of the box, as a function of x, is V = V(x) = which, after distributing, simplifies to V : V(x) = To determine the value of x that corresponds to a maximum volume, we need to find V'. V' Solving V' = 0 → x = inches and the maximum volume is V cubic inches

Q: 5. This box has a length x and a width that is 4 times its length. The volume is 500 cm. Find a…

A: Given length is xWidth is 4 times length = 4*xVolume is 500 cm3We know that volume of a cuboid is…

Q: Pure Water Enterprises finds that the marginal profit, in dollars, from drilling a well that is x…

A: The marginal profit is defined as the first order derivative of the profit function. So, we can…

Q: Differentiate the function. √/t+6√3 u' = = n 7/ X

A:

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: Illustrate the following functions:. S(1, y) = 4 – x² – y², g(x, y); x² + y² What is the shape of…

A: given two functions fx,y=4-x2-y2gx,y=1x2+y2   now, we will draw the contour lines of each of them…

Q: Determine where the function is concave upward and where it is concave downward. g (x) = 5+ 22…

A: We have to choose the correct answer from the given option according to the given function

Q: 1. The function f gives the discharge rate of the Kalamazoo river in m³/s as a function of x miles…

A:

Q: Find the derivative of f(x) = x In(x) 1- In(x) O In(x) O1+ In(x) O In(x) /x

A:

Q: Suppose that Evelyn’s utility function is given as: U(x,y) = xy Evelyn has an income of Php 100.…

A: Given: Evelyn's utility function is given as U(x,y) = xy Evelyn has an income of Php 100.  The…

Q: 9x +18 da 18 9x+ 7x7 6. 9x 7r7 18 9x + 18 7x7 18 9r + 11r7

A: Given: I=∫9x8+18x8dx We know that the Power rule; ∫xndx=xn+1n+1+C ; n≠-1

Q: 1. (8 pts) For the function f (x) = 1 – 2x², find: а. f (x + h) b. f(x + h) – f(x) f(x+h)-f(x) С. h

A: From the given problem:   fx=1-2x2   a.   fx+h=1-2x+h2=1-2x2+2xh+h2=1-2x2-4xh-2h2   b.…

Q: How do you find the domain and range for f(x,y) = ln(x+y)?

A: The given function:

Q: The monthly demand function and cost function for x newspapers at a newstand are given p=10-0.002x…

A:

Q: Find f. f"(x) = 4x3 – 6x² + 5, f(2) = 1, f'(3) = 2 %3D

A: Here, f''(x)=4x3-6x2+5⇒f'(x)=∫(4x3-6x2+5)dx+C             =4x44-6x33+5x+C             =x4-2x3+5x+C…