Chapter 11.3, Problem 59E

### 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 product at $p per unit is given by p ( q + 1 ) 2 = 200 , 000 find the rate of change of quantity with respect to price when p =$80. Interpret this result.

To determine

To calculate: The rate of change of quantity with respect to price when p=$80 and the demand function for q units of a production at$p per unit is given by p(q+1)2=200,000.

Explanation

Given Information:

The demand function for q units of a production at $p per unit is given by, p(q+1)2=200,000. Formula used: According to the product rule of derivatives, ddx(uv)=udvdx+vdudx. Calculation: As it is provided that the demand function for q units of a production at$p per unit is given by:

p(q+1)2=200,000.

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,

ddp(p(q+1)2)=ddp(200,000)

To find the derivative of the above expression,

ddp(p(q+1)2)=ddp(200,000)pddp(q+1)2+(q+1)2ddp(p)=02p(q+1)dqdp+(q<

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