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Question

The absolute difference between the greatest and the least values of the function f(x)=x(lnx2) on [1,e2] is

A
2
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B
e
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C
e2
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D
1
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Solution

The correct option is B e
f(x)=x(lnx2)
f(x)=x(1x)+(lnx2)=lnx1
f(x)=lnx1
f(x)=0x=e
For x[1,e), f(x)<0 and for x(e,e2], f(x)>0
So, the minimum value of f(x) occurs at x=e

Now, f(1)=2
f(e)=e (least)
f(e2)=0 (greatest)

Hence, |f(e2)f(e)|=|0(e)|=e

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