(a) Explanation Given: I ( x ) = − 68 x 2 + 7480 x − 118000 ( 25 ≤ x ≤ 75 ) , Formula used: Write the formula for derivative of power rule. If f ( x ) = x n for any number n , then the derivative. f ′ ( x ) = n x n − 1 If f ( x ) = k for any real number k , then the derivative is defined by the formula. f ′ ( x ) = 0 Calculation: To find the years, where the average adjusted gross income increasing, take the derivative of the income function with respect to x . I ′ ( x ) = − 68 ( 2 ) x + 7480 = − 136 x + 7480 …… (1) Because for every x , the derivative exists. Find the point where the derivative is zero also known as the critical point. Substitute 0 for I ′ ( x ) . − 136 x + 7480 = 0 − 136 x = − 7480 Solve the point (b) To determine The ages where the average adjusted gross income decreasing, from the given income function. (c) To determine The all local extrema from the give income function.

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 12, Problem 51RE

(a)

To determine

To Calculate: The ages where the average adjusted gross income is increasing from the given income function.

(b)

To determine

The ages where the average adjusted gross income decreasing, from the given income function.

(c)

To determine

The all local extrema from the give income function.

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Chapter 12, Problem 50RE

Chapter 12, Problem 52RE

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Chapter 12 Solutions

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

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

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The ages where the average adjusted gross income is increasing from the given income function.

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To Calculate: The ages where the average adjusted gross income is increasing from the given income function.

The ages where the average adjusted gross income decreasing, from the given income function.

The all local extrema from the give income function.

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