   Chapter 9.3, Problem 49E ### 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 Suppose that the profit function for the monthly sales of a car by a dealership is P ( x ) = 500 x − x 2 − 100 where x is the number of cars sold. What is the instantaneous rate of change of profit when(a) 200 cars are sold? Explain its meaning.(b) 300 cars are sold? Explain its meaning.

(a)

To determine

To calculate: The instantaneous rate of change of profit and its meaning when 200 cars are sold if the profit for monthly sales of a car is given by

P(x)=500xx2100

where x is the number of cars sold.

Explanation

Given Information:

200 cars are sold and the profit for monthly sales of a car is given by

P(x)=500xx2100

where x is the number of cars sold.

Formula used:

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

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

Calculation:

Consider the provided statement,

200 cars are sold if the profit for monthly sales of a car is given by

P(x)=500xx2100

where x is the number of cars sold.

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

P(x+h)=500(x+h)(x+h)2100=500x+500h(x2+h2+2xh)100=500x+500hx2

(b)

To determine

To calculate: The instantaneous rate of change of profit and its meaning when 300 cars are sold if the profit for monthly sales of a car is given by

P(x)=500xx2100

where x is the number of cars sold.

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