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Question

If f(x)=x2ex2/a2 is an increasing function then (for a>0), x lies in the interval

A
[a,2a]
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B
(,a)(0,a)
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C
(a,0)
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D
None of these
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Solution

The correct option is B (,a)(0,a)
For a function f(x) to be increasing, f(x)>0
f(x)=x2ex2/a2
ln(f(x))=2lnxx2a2
f(x)f(x)=2x2xa2
f(x)=2f(x)a2(a2x2x)
(f(x)>0 x
f(x)a2x2x>0
x(,a)(0,a)


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