Explanation Given: The function C ( x ) = 1 2 x 3 + 2 x 2 − 3 x + 35 . Calculation: The average cost function is C ¯ ( x ) = C ( x ) x . Substitute C ( x ) = 1 2 x 3 + 2 x 2 − 3 x + 35 in the above equation. C ¯ ( x ) = 1 2 x 3 + 2 x 2 − 3 x + 35 x = 1 2 x 2 + 2 x − 3 + 35 x Calculate C ′ ¯ ( x ) to find the point where the average cost function is smallest. C ¯ ( x ) = 1 2 x 2 + 2 x − 3 + 35 x C ¯ ′ ( x ) = 1 2 ( 2 x ) + 2 ( 1 ) − 0 + 35 ( − 1 x 2 ) = x + 2 − 35 x 2 Use online graphing calculator to draw the graph of the function C ¯ ′ ( x ) = x + 2 − 35 x 2 is as shown below in Figure 1

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ISBN: 2818440028601

Author: Lial

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Chapter 6.2, Problem 5E

To determine

The average cost function and also to find where the average cost is smallest and derivative of the cost function is zero.

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Chapter 6.2, Problem 4E

Chapter 6.2, Problem 6E

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Chapter 6 Solutions

CALCULUS WITH APPLICATIONS

Ch. 6.1 - YOUR TURN 1 Find the absolute extrema of the...Ch. 6.1 - Prob. 2YT Ch. 6.1 - Prob. 1WE Ch. 6.1 - Prob. 2WE Ch. 6.1 - Prob. 1E Ch. 6.1 - Find the locations of any absolute extrema for the...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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