(a) Explanation Given Information: The demand function is D ( p ) = 50000 p 2 − 1 2 and the price is p = 50 . 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 ) = x n , then f ′ ( x ) = n x n − 1 . 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 ) = c ⋅ u ( x ) , where u ( x ) is a differentiable function of x , then f ′ ( x ) = c ⋅ u ′ ( x ) . Calculation: Consider the demand function as D ( p ) = 50000 p 2 − 1 2 (b) To determine To calculate: The instantaneous rate of change of demand with respect to price for the demand function D ( p ) = 50000 p 2 − 1 2 for p = 100 , and meaning of it.

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ISBN: 9781305713864

Author: HARSHBARGER

Publisher: CENGAGE L

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Chapter 9.4, Problem 52E

(a)

To determine

To calculate: The instantaneous rate of change of demand with respect to price for the demand function D(p)=50000p2−12 at p=50, and also meaning of it.

(b)

To determine

To calculate: The instantaneous rate of change of demand with respect to price for the demand function D(p)=50000p2−12 for p=100, and meaning of it.

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Chapter 9.4, Problem 51E

Chapter 9.4, Problem 53E

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Chapter 9 Solutions

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The instantaneous rate of change of demand with respect to price for the demand function D ( p ) = 50000 p 2 − 1 2 at p = 50 , and also meaning of it.

Solution Summary: The author calculates the instantaneous rate of change of demand with respect to price for the demand function D(p)=50000p

To calculate: The instantaneous rate of change of demand with respect to price for the demand function D(p)=50000p2−12 at p=50, and also meaning of it.

To calculate: The instantaneous rate of change of demand with respect to price for the demand function D(p)=50000p2−12 for p=100, and meaning of it.

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Chapter 9 Solutions