   Chapter 9.5, Problem 48E ### 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

# Advertising and sales The sales of a product s (in thousands of dollars) are related to advertising expenses (in thousands of dollars) by s = 200 x x + 10 Find and interpret the meaning of the rate of change of sales with respect to advertising expenses when(a) x   =   10 . (b) x =   20 .

(a)

To determine

To calculate: The rate of change of sales with respect to advertising expenses x (in thousands of dollars) if the sales of a product s (in thousands of dollars) are related to advertising expenses $10,000 is s=200xx+10. Explanation Given Information: The sales of a product s are related to advertising expenses x by s=200xx+10 and the advertising expenses is 10 thousand of dollars. Formula Used: The quotient rule for the derivative of the two function, ddx(fg)=gdfdxfdgdxg2. The sum and difference rule of derivate of functions, ddx[u(x)±v(x)]=ddxu(x)±ddxv(x). The simple power rule of derivative ddx(xn)=nxn1. Calculation: Consider the sale of a product, s=200xx+10. Differentiate the provided sale function with respect to x. dsdx=ddx(200xx+10) Use the quotient rule for the derivative of the two function f(x) and g(x) is, ddx(fg)=gdfdxfdgdxg2. dsdx=(x+10)ddx(200x)(200x)ddx(x+10)(x+10)2 Use the sum and difference rule of derivative, ddx[u(x)±v(x)]=ddxu(x)±ddxv(x) (b) To determine To calculate: The rate of change of sales with respect to advertising expenses x (in thousands of dollars) if the sales of a product s (in thousands of dollars) are related to advertising expenses at$20,000 is s=200xx+10.

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