   Chapter 9.4, Problem 52E ### 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

# Demand Suppose that the demand tor a product depends on the price p according to D ( p ) = 50 , 000 p 2 − 1 2 ,  p>0 where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when(a) p = 50. (b) p = 100.

(a)

To determine

To calculate: The instantaneous rate of change of demand with respect to price for the demand function D(p)=50000p212 at p=50, and also meaning of it.

Explanation

Given Information:

The demand function is D(p)=50000p212 and the price is p=50.

Formula Used:

According to sum rule of derivatives,

If

f(x)=u(x)+v(x)

Then,

f(x)=u(x)+v(x)

According to power rule,

If f(x)=xn, then f(x)=nxn1.

According to constant function rule,

If f(x)=c, then f(x)=0.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Calculation:

Consider the demand function as D(p)=50000p212

(b)

To determine

To calculate: The instantaneous rate of change of demand with respect to price for the demand function D(p)=50000p212 for p=100, and meaning of it.

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