   Chapter 10.3, Problem 7E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# If the total revenue function for a computer is R ( x ) =   2000 x − 20 x 2 − x 3 , find the level of sales, x, that maximizes revenue and find the maximum revenue in dollars.

To determine

To calculate: The maximum revenue of the provided revenue function R(x)=2000x20x2x3 and the unit for which it is maximum.

Explanation

Given Information:

The provided revenue function is:

R(x)=2000x20x2x3

Formula used:

If f(x) and g(x) are two differentiable functions then by the property of derivative:

ddx(f(x)+g(x))=ddxf(x)+ddxg(x)

And,

ddxxn=nxn1

Where n is a constant and x is the variable.

Calculation:

The absolute maxima and absolute minima will occur only at the critical points. To calculate the critical points of the provided function find the first derivative of the function:

R=2000x20x2x3ddxR=ddx(2000x20x2x3)

Use ddx(f(x)+g(x))=ddxf(x)+ddxg(x)

R(x)=ddx2000xddx20x2ddxx3

Now use ddxxn=nx

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