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The maximum value of x^4ehat-x^2 is e^2 ...

The maximum value of `x^4ehat-x^2` is `e^2` (b) `e^(-2)` (c) `12 e^(-2)` (d) `4e^(-2)`

A

`e^(2)`

B

`e^(-2)`

C

`12e^(-2)`

D

`4e^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
4
f(X)=`x^(4)e^(-x^(2))`
or `f(x) =4x^(3)e^(-x^(2))+x^(4)e^(-x^(2))(-2x)`
`=2x^(3)e^(-x)(2-x^(2))`
sign scheme of f(X) is as follows

Hence f(X) is maximum at `x=pm sqrt(2)` Thus maximum value =`4e^(-2)`
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