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Chapter 9.9, Problem 6CP
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### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# If the total profit function for a product is P ( x ) = 20 x + 1 − 2 x − 22 , then the marginal profit and its derivative are M P ¯ = p ' ( x ) 10 x + 1 − 2  and  p " ( x ) = − 5 ( x + 1 ) 3 Is P " ( x ) < 0 for all values of x ≥ 0 ?

To determine

The validity of the P(x)<0 for all values of x such that x0, if the profit function is P(x)=20x+12x22, marginal profit P(x)=10x+12, and P(x)=10x+12.

Explanation

Given Information:

The total profits of a product are represented by the function, P(x)=20x+1âˆ’2xâˆ’22. The marginal profit of the function is MPÂ¯=Pâ€²(x)=10x+1âˆ’2 and the derivative of the marginal profit is represented as, Pâ€²â€²(x)=âˆ’5(x+1)3.

Explanation:

Consider the provided profit function,

P(x)=20x+1âˆ’2xâˆ’22

The marginal profits of a function represent the profits earned by selling an additional unit of a commodity

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