Mean Value theorem problem?(inequality) I'm trying to solve this mean value theorem problem but con

deformere692qr

deformere692qr

Answered question

2022-05-13

Mean Value theorem problem?(inequality)
I'm trying to solve this mean value theorem problem but confused where to start,
If 0 < a < b prove that ( 1 a b ) < ln b a < b a 1
Can someone please lend me a hand?

Answer & Explanation

stafninumfu1tf

stafninumfu1tf

Beginner2022-05-14Added 18 answers

Apply the mean value theorem to the function x ln x on the interval [ a , b ]: c ( a , b ) such that
1 b a = b a b < ln b ln a = ln b a = ( b a ) 1 c < b a a = b a 1
datomerki8a5yj

datomerki8a5yj

Beginner2022-05-15Added 5 answers

HINT :
1 a b < ln b ln a < b a 1
1 a b b a < ln b ln a b a < b a 1 b a
b a b ( b a ) < ln b ln a b a < b a a ( b a )

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