To determine To calculate: The cost function, C ( x ) . Explanation Given: The marginal cost function is C ′ ( x ) = 2 x 3 + 6 x − 5 and fixed cost is C ( 0 ) = $ 800 . Formula used: The family of all anti-derivatives of the function f is denoted by ∫ f ( x ) d x . If F ′ ( x ) = f ( x ) , then ∫ f ( x ) d x = F ( x ) + C , for any real number C . Power rule of anti-derivatives is defined as: For any real number n ≠ − 1 , ∫ x n d x = 1 n + 1 x n + 1 + C Let f ( x ) and g ( x ) be functions that have anti-derivatives and let k be any real number. Constant Multiple Rule is: ∫ k f ( x ) d x = k ∫ f ( x ) d x Sum or difference rule is: ∫ [ f ( x ) ± g ( x ) ] d x = ∫ f ( x ) d x ± ∫ g ( x ) d x Calculation: Since C ′ ( x ) gives the rate of change of ‘ x ’. The cost function, C( x ) is calculated as: C ( x ) = ∫ C ′ ( x ) d x = ∫ ( 2 x 3 + 6 x − 5 ) d x Integrate using sum or difference rule to get: C ( x ) = ∫ ( 2 x 3 + 6 x − 5 ) d x

Mathematics with Applications and Mylab Math with Pearson EText -- Title-Specific Access Card Package

12th Edition

ISBN: 9780134862668

Author: Lial, Margaret L.

Publisher: Pearson Education Canada

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Chapter 13.1, Problem 8CP

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To calculate: The cost function, C(x).

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Mathematics with Applications and Mylab Math with Pearson EText -- Title-Specific Access Card Package

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

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