Let `f(x)` be a real valued continuous function on `R` defined as `f(x)=x^2e^(-|x|)` The value of `k` for which the curve `y=k x^2(k >0)` intersect the curve `y=e^(|x|)` at exactly two points, is `e^2` (b) `(e^2)/2` (c) `(e^2)/4\ ` (d) `(e^2)/8`

Options

A. `(e^(2))/4ltkltoo`
B. `(e^(2))/2`
C. `(0ltklt=4)/(e^(2))`
D. `(e^(2))/4`

Answer

A, D

Explanation

Graph of `f(x)`
`y=kx^(2)` will intersect `y=e^(|x|)`
Then `kx^(2)=e^(|x|)`
`x^(2)e^(|x|)=1/kimplies1/k=4/(e^(2))impliesk=(e^(2))/4`