   Chapter 9.9, Problem 26E ### 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

# In Problems 25-28, cost, revenue, and profit are in dollars and X is the number of units.If the total profit function is P ( x ) =   16 x   −   32 , find the marginal profit. What does this mean?

To determine

To calculate: The marginal profit, for the profit function, P(x)=16x32 and the meaning of the result.

Explanation

Given Information:

The profit function is P(x)=16x32.

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

The derivative of a constant value, k, is

ddx(k)=0

Calculation:

Consider the marginal profit function to be MP¯. Consider the provided profit function,

P(x)=16x32

The marginal profit of a profit function is found by differentiating the cost function

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