Explanation Given information: The function is y = x 2 3 − x . Calculation: Write the given function. y = x 2 3 − x (1) Find the domain of function y . The input of y consists of all values of x for which the function 3 − x is nonnegative. 3 − x is nonnegative refers that 3 − x ≥ 0 or x ≤ 3 . Hence, the value of x is − ∞ to 3. Therefore, the domain of function is − ∞ < x < 3 _ . Find the first derivative [ y ′ ] of given function. y ′ = x 2 2 3 − x ( − 1 ) + 2 x 3 − x = − x 2 2 3 − x + 2 x 3 − x = − x 2 + 4 x ( 3 − x ) 2 3 − x = − x 2 + 12 x − 4 x 2 2 3 − x = − 5 x 2 + 12 x 2 3 − x (2) At the critical point, the first derivative of y is zero or undefined Find the critical point of function y . Case 1. − 5 x 2 + 12 x 2 3 − x = 0 − 5 x 2 + 12 x = 0 5 x 2 = 12 x 5 x = 12 x = 12 5 Case 2. − 5 x 2 + 12 x 2 3 − x = 0 − 5 x 2 + 12 x = 0 x ( − 5 x + 12 ) = 0 x = 0 At x = 3 , the derivative y ′ is undefined

University Calculus: Early Transcendentals Plus MyLab Math -- Access Card Package (3rd Edition) (Integrated Review Courses in MyMathLab and MyStatLab)

3rd Edition

ISBN: 9780321999573

Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 4.1, Problem 72E

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Find the critical points, domain endpoints and extreme values for given function.

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Chapter 4.1, Problem 71E

Chapter 4.1, Problem 73E

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University Calculus: Early Transcendentals Plus MyLab Math -- Access Card Package (3rd Edition) (Integrated Review Courses in MyMathLab and MyStatLab)

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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