Find the global maximum and minimum for the function on the closed interval. Show your work and justify your answer. A calculator answer is not acceptable. f(x)=x-2 ln(x+1), where 0<= x<=2

Cherish Rivera

Cherish Rivera

Answered question

2022-11-30

Find the global maximum and minimum for the function on the closed interval. Show your work and justify your answer. A calculator answer is not acceptable.
f ( x ) = x 2 ln ( x + 1 ) ,  where  0 x 2

Answer & Explanation

Beckham Krueger

Beckham Krueger

Beginner2022-12-01Added 7 answers

Solution:
f ( x ) = x 2 ln ( x + 1 ) 0 x 2 f ( x ) = 1 2 ( 1 x + 1 ) = x + 1 2 x + 1 f ( x ) = x 1 x + 1 f ( x ) = 0 x 1 x + 1 = 0 x = 1
Global maximum = max { f ( 0 ) , f ( 1 ) , f ( 2 ) } = max { 0 , 0.386 , 0.197 }
Global maximum =0 at x=0

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