Explanation Given information: Show the function as follows: f ( x ) = 2 e x ( 1 + x 2 ) (1) Calculation: Fid the derivative of the function f ( x ) as follows: f ′ ( x ) = d d x ( 2 e x ( 1 + x 2 ) ) = ( 1 + x 2 ) d d x 2 e x − 2 e x d d x ( 1 + x 2 ) ( 1 + x 2 ) 2 = ( 1 + x 2 ) × 2 e x − 2 e x × 2 x ( 1 + x 2 ) 2 = ( 1 + x 2 − 2 x ) × 2 e x ( 1 + x 2 ) 2 f ′ ( x ) = ( 1 − x ) 2 × 2 e x ( 1 + x 2 ) 2 (2) Find the critical point of the function f ( x ) as follows: Equate the derivative f ′ ( x ) to zero

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 4, Problem 22PE

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Find whether the function f(x) have an absolute maximum value and/or absolute minimum value, give reason if these values does not exist.

Write down the critical points of the function f.

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Chapter 4, Problem 21PE

Chapter 4, Problem 23PE

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Chapter 4 Solutions

University Calculus: Early Transcendentals (4th Edition)

Ch. 4.1 - In Exercises 16, determine from the graph whether...Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 3E Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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Find whether the function f ( x ) have an absolute maximum value and/or absolute minimum value, give reason if these values does not exist. Write down the critical points of the function f .

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Find whether the function f(x) have an absolute maximum value and/or absolute minimum value, give reason if these values does not exist. Write down the critical points of the function f.

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Chapter 4 Solutions

Find whether the function f(x) have an absolute maximum value and/or absolute minimum value, give reason if these values does not exist.

Write down the critical points of the function f.