   Chapter 9.3, Problem 50E ### 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

# Profit It the total revenue function and the total cost function for a toy are R ( x ) = 2 x  and  C ( x ) = 100 + 0.2 x 2 + x what is the instantaneous rate of change of profit if 10 units are produced and sold? Explain its meaning.

To determine

To calculate: The instantaneous rate of change of profit and its meaning when 10 units are produced and sold if the total revenue and cost function are given by

R(x)=2xC(x)=100+0.2x2+x

Explanation

Given Information:

10 units are produced and sold. The total revenue and cost function are given by

R(x)=2xC(x)=100+0.2x2+x

Formula used:

If a function f(x) is defined in the interval [x,x+h], then its instantaneous rate of change is given by the derivative as

f(x)=limh0f(x+h)f(x)h

Profit is the difference of the revenue obtained and the total cost. The formula for profit is

P(x)=R(x)C(x)

Calculation:

Consider the provided statements,

10 units are produced and sold. The total revenue and cost function are given by

R(x)=2xC(x)=100+0.2x2+x

Apply the formula of profit function P(x)=R(x)C(x),

P(x)=2x(100+0.2x2+x)=2x1000.2x2x=x1000.2x2

Substitute x=x+h in P(x) to get,

P(x+h)=(x+h)1000

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