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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Checkpoint 6 Worked-out solution available at LarsonAppHadCakulus.com

The marginal profit for a product is modeled by

d P d x =   0.0002 x   +   14.2 .

a. Find the change in profit when sales increase from 100 to 101 units.

b. Find the change in profit when sales increase from 100 to 110 units.

(a)

To determine

To calculate: The change in profit P in marginal function dPdx=0.0002x+14.2 for number of units x=100 while x increases by x=101.

Explanation

Given information:

The marginal function dPdx=0.0002x+14.2 for number of units x=100 while x increases by x=101.

Formula used:

According to the fundamental theorem of calculus.

abf(x) dx=F(b)F(a)

For a function F when F(x)=f(x) and function f is continuous on [a,b].

Calculation:

Consider the marginal function dPdx=0.0002x+14.2.

The change in the profit obtained by increasing from 100 to 101 units is

100101dPdxdx=1001010

(b)

To determine

To calculate: The change in profit P in marginal function dPdx=0.0002x+14.2 for number of units x=100 while x increases by x=110.

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