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