Chapter 9, Problem 91RE

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Demand Suppose that the demand for x units of a product is given by x =   ( 100 / p )   −   1 , where p is the price per unit of the product. Find and interpret the rate of change of demand with respect to price if the price is(a) $10.(b)$20.

(a)

To determine

To calculate: The rate of change of demand with respect to price when the price is $10 and the demand function is x=(100p)1, where p is the price of the product, and what the value of the rate of change means. Explanation Given Information: The demand function is represented as x=(100p)1, where p is the price of the product. Formula used: According to the power rule of derivatives, ddx(xn)=nxn1 According to the property of derivatives, the derivative of a constant value c is ddx(c)=0 Calculation: Consider the provided demand function, x=(100p)1 To find the rate of change, differentiate both sides with respect to p, dxdp=ddp(100p1)=ddp(100p)ddp(1) (b) To determine To calculate: The rate of change of demand with respect to price when the price is$20 and the demand function is x=(100p)1, where p is the price of the product, and what the value of the rate of change means.

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