(a)$25Interpret the instantaneous rate of change.When asked to find the instantaneous rate of change of demand with respect to price at various prices, we are being asked to find the first derivative of the demand equation q = 500 p − 1 and evaluate the derivative at the given prices.Recall the Powers of x Rule: If f(x) = xn where n is a real number, then f '(x) = nxn − 1.Before we can find the derivative of q with respect to p, the demand equation must be rewritten so the Powers of x Rule can be applied. First convert from radical to exponential form, and then rewrite so the variable is not in the denominator.q = 500 p − 1 = 500p1/2 − 1 = 500 − 1

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Answered: (a) $25 Interpret the instantaneous…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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(a)

$25

Interpret the instantaneous rate of change.

When asked to find the instantaneous rate of change of demand with respect to price at various prices, we are being asked to find the first derivative of the demand equation

q =

500

− 1

and evaluate the derivative at the given prices.

Recall the Powers of x Rule: If

f(x) = xⁿ

where n is a real number, then

f '(x) = nx^n − 1.

Before we can find the derivative of q with respect to p, the demand equation must be rewritten so the Powers of x Rule can be applied. First convert from radical to exponential form, and then rewrite so the variable is not in the denominator.

500

− 1