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Question

# Let f(x)=x2.e−x2 then

A
f(x) has local maxima at x = -1 and x = 1
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B
f(x) has local minima at x = 0
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C
f(x) is strictly decreasing on x ϵ R
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D
Range of f(x) is [0,1e]
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Solution

## The correct options are A f(x) has local maxima at x = -1 and x = 1 B f(x) has local minima at x = 0 D Range of f(x) is [0,1e]f(x)=x2.e−x2 f′(x)=2x.e−x2+x2.e−x2(−2x) =2xe−x2[1−x2] f(x) has local maxima at x = -1 and 1 f(x) has local minima at x = 0 Now; f(0) = 0 f(1)=1e and as x→∞, f(x)→0 So, Range of f(x) is (0,1e).

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