   Chapter 10.3, Problem 8E ### 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

# A firm has total revenues given by R ( x ) =2800 x − 8 x 2 − x 3 dollars for x units of a product. Find the maximum revenue from sales of that product.

To determine

To calculate: The maximum revenue of the provided revenue function R(x)=2800x8x2x3 and the unit for which it is maximum.

Explanation

Given Information:

The provided revenue function is:

R(x)=2800x8x2x3

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 an 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=2800x8x2x3ddxR=ddx(2800x8x2x3)

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

R(x)=ddx2800xddx8x2ddxx3

Now use ddxxn=n</

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