Explanation Given Information: The average cost is decreasing. Consider the function, C ( x ) = 500 x − 60 As marginal cost is C ′ ( x ) So, calculate the average cost if the function, C ′ ( x ) = d d x ( 500 x − 60 ) Difference rule of the derivative is d d x [ f ( x ) − g ( x ) ] = d d x [ f ( x ) ] − d d x [ g ( x ) ] where f ( x ) and g ( x ) are any two differentiable functions. Constant multiple rules of the derivative are f ′ ( c x ) = c f ′ ( x ) , where c is any constant. Apply sum rule and constant multiple rules of the derivative in C ′ ( x ) = d d x ( 500 x − 60 ) , C ′ ( x ) = 500 d d x ( x ) − 60 d d x ( 1 ) A derivative of a function y = x n using power rule is d y d x = n x n − 1

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ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 4.2, Problem 44E

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Whether the marginal cost is necessarily decreasing if the average cost is decreasing and explain the answer.

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Chapter 4.2, Problem 43E

Chapter 4.2, Problem 45E

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Chapter 4 Solutions

Applied Calculus

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Whether the marginal cost is necessarily decreasing if the average cost is decreasing and explain the answer.

Solution Summary: The author explains that the marginal cost isn't decreasing if the average cost's decreasing. A derivative of a constant is 0.

Whether the marginal cost is necessarily decreasing if the average cost is decreasing and explain the answer.

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Chapter 4 Solutions