(a) To determine To find: The absolute extrema of the function f ( x ) = 2 ln x x 2 for the interval [ 1 , 4 ] . Explanation The given function is f ( x ) = 2 ln x x 2 and interval is [ 1 , 4 ] . Find the critical number in the interval [ 1 , 4 ] to compute the absolute minimum and absolute maximum. Differentiate the function f ( x ) = 2 ln x x 2 as follows. f ′ ( x ) = d d x ( 2 ln x x 2 ) = ( x 2 ) 2 ( 1 x ) − 2 ln x ( 2 x ) ( x 2 ) 2 = 2 x − 4 x ln x x 4 = 2 x ( 1 − 2 ln x ) x 4 That is, f ′ ( x ) = 2 ( 1 − 2 ln x ) x 3 . Set f ′ ( x ) = 0 and solve for x . 2 − 4 ln x x 3 = 0 2 − 4 ln x = 0 2 = 4 ln x 0.5 = ln x On simplifying further, x = e 0.5 x ≈ 1 .6487 Hence, the critical numbers is x = 1 (b) To determine To find: The absolute extrema of the function f ( x ) = 2 ln x x 2 for the interval [ 2 , 5 ] .

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 6, Problem 17RE

(a)

To determine

To find: The absolute extrema of the function f(x)=2lnxx2 for the interval [1,4] .

(b)

To determine

To find: The absolute extrema of the function f(x)=2lnxx2 for the interval [2,5] .

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Chapter 6, Problem 16RE

Chapter 6, Problem 18RE

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Chapter 6 Solutions

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

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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