Chapter 11.3, Problem 60E

### 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 If the demand function for q units of a commodity at $p per unit is given by p 2 ( 2 q + 1 ) = 100 , 000 find the rate of change of quantity with respect to price when p=$50. Interpret this result.

To determine

To calculate: The rate of change of quantity with respect to price when p=$50 and the demand function for q units of a production at$p per unit is given by p2(2q+1)=100,000.

Explanation

Given Information:

The demand function for q units of a production at $p per unit is given by: p2(2q+1)=100,000. Formula used: According to the product rule of derivatives, ddx(uv)=udvdx+vdudx. Calculation: As it is provided that the demand function for q units of a production at$p per unit is given by:

p2(2q+1)=100,000.

Now, the rate of change of quantity with respect to price is given by dqdp.

Now, differentiate both sides of equation with respect to p to get:

ddp(p2(2q+1))=ddp(100,000)

To obtain the derivative of 2q+1 as,

ddp(p2(2q+1))=ddp(100,000)2p2dqdp+(2q+1)(2p)

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