Chapter 9, Problem 97RE

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# Supply The number of units x of a product that is supplied at price p is given by x = p − 1 , p ≥ 1 If the price p is $10, what is the rate of change of the supply with respect to the price, and what does it tell us? To determine To calculate: The rate of change of supply when the price is$10, with the supply function represented by, x=p1, for a product with price p and the meaning of the value.

Explanation

Given Information:

The provided function for supply is x=p1, where p is the price.

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

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

According to the chain rule of derivatives, for a function of form, y=f(u(x)), the derivative is

dydx=f(u(x))u(x)

Calculation:

Consider the provided supply function,

x=p1

Rewrite the function,

x=(p1)12

To find the rate of change of supply, differentiate both sides with respect to p,

dxdp=dd<

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