Chapter 9.4, Problem 51E

### 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 The demand for q units of a product depends on the price p (in dollars) according to q = 1000 p − 1 ,  for  p  > 0 Find and explain the meaning of the instantaneous rate of change of demand with respect to price when the price is(a) $25. (b)$100.

(a)

To determine

To calculate: The instantaneous rate of change of demand with respect to price for the demand function q(p)=1000p1 for p=25, and also find its meaning.

Explanation

Given Information:

The demand function, q(p)=1000p1 and the price is p=25.

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 given demand function q(p)=1000p1.

The instantaneous rate of change of demand with respect to price which is dq(p)dp

(b)

To determine

To calculate: The instantaneous rate of change of demand with respect to price for the demand function q(p)=1000p1 at p=100, and meaning of it.

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