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find the max. & min. value of f(x)=x ln 2 x

find the max. & min. value of f(x)=x ln2x

Grade:12

1 Answers

askiitian.expert- chandra sekhar
10 Points
12 years ago

Hi Upendra,

f(x)=x ln2x ; x>0

f1(x)=x 2 lnx (1/x) + ln2x

         = 2 ln x + ln2x = ln x (lnx+2)

for max or min f1(x) = 0

     x=1 or e-2

f11(x) = 2/x + (2/x) ln x = (2/x)(lnx+1)

at x=1; f11(x) = 2 >0

at x=e-2 ; f11(x) = -2 e2<0

therefore f(x) is max at x=e-2

and minimum at x=1

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