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

Options

A. `e^(2)`
B. `e^(-2)`
C. `12e^(-2)`
D. `4e^(-2)`

Answer

4

Explanation

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)`