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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

Effect of Advertising on Profit The quarterly profit (in thousands of dollars) of Cunningham Realty is given by

P(x) = − 1 3 x2 + 7x + 30 (0 ≤ x ≤ 50)

where x (in thousands of dollars) is the amount of money Cunningham spends on advertising per quarter.

  1. a. Find P(x).
  2. b. What is the rate of change of Cunningham’s quarterly profit if the amount it spends on advertising is $10,000 quarter (x = 10) and $30,000 quarter (x = 30)?

(a)

To determine

To find: The value of P(x) .

Explanation

Given information:

The quarterly profit (in thousands of dollars) of Cunningham reality is,

P(x)=13x2+7x+30   (0x50) (1)

Calculation:

Differentiate equation (1) with respect to x and calculate the value of P(x) ,

P(x)=ddx(13x2+7x+30)=13ddxx2+7ddxx+ddx30(ddx(x+y+z)=ddx

(b)

To determine

The rate of change of Cunningham quarterly profit at x=10 and x=30 .

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P-23RECh-2 P-24RECh-2 P-25RECh-2 P-26RECh-2 P-27RECh-2 P-28RECh-2 P-29RECh-2 P-30RECh-2 P-31RECh-2 P-32RECh-2 P-33RECh-2 P-34RECh-2 P-35RECh-2 P-36RECh-2 P-37RECh-2 P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-55RECh-2 P-56RECh-2 P-57RECh-2 P-58RECh-2 P-59RECh-2 P-60RECh-2 P-61RECh-2 P-62RECh-2 P-63RECh-2 P-64RECh-2 P-1BMCh-2 P-2BMCh-2 P-3BMCh-2 P-4BMCh-2 P-5BMCh-2 P-6BM

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