Chapter 7.5, Problem 55ES

The total cost C (in dollars) of purchasing and maintaining a piece of equipment for x years is represented by the following. X. C(x) : 6000 36 + 2 Jo (a) Perform the integration to write C as a function of x. C(x) = (b) Find C(1), C(5), and C(10). (Round your answers to the nearest whole number.) C(1) = $ C(5) = $ C(10) = $

From a rectangular piece of cardboard having dimensions a × b, where a = 10 inches and b = 20 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the figure). Express the volume V of the box as a function of x. V(x) =?

Find two numbers whose sum is 42 and whose product is as large as possible.​ [Hint: Let x and 42−x be the two positive numbers. Their product can be described by the function f(x)=​x(42−​x).]