(a) Explanation Given information: The demand function for the sports watch is, d ( x ) = 50 0.01 x 2 + 1 ( 0 ≤ x ≤ 20 ) (1) In the above equation x is the quantity demanded per week in units of thousand and d ( x ) is the unit price in dollars. Formula used : The quotient rule of differentiation is, f ′ ( x ) = d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) [ g ( x ) ] 2 The above formula is defined when the denominator g ( x ) ≠ 0 . Calculation: Use the quotient rule of differentiation for the equation (1) to get the derivative function d ′ ( x ) . d ′ ( x ) = d d x [ 50 0.01 x 2 + 1 ] = = ( 0 (b) To determine To find: The values of derivative functions d ′ ( 5 ) , d ′ ( 10 ) , d ′ ( 15 ) and interpret the result.

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Question

Chapter 3.2, Problem 56E

(a)

To determine

To find: The derivative function d′(x) .

(b)

To determine

To find: The values of derivative functions d′(5) , d′(10) , d′(15) and interpret the result.

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Chapter 3.2, Problem 55E

Chapter 3.2, Problem 57E

Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The derivative function d ′ ( x ) .

Solution Summary: The author explains how to calculate the derivative function dprime(x).