Find the coordinates of the point of inflection of the curve f(x) `=e^(-x^(2))`

Explanation

We have f(x) =`e^(-x^(2))`
`therefore f(x)=-2xe^(-x^(2))`
`rArr f(x)=-2e^(-x^(2)).1+x.e^(-x^(2))(-2x)`
If f(x)=0 then `2e^(-x^(2))(2x-1)=0`
`rArr x=+(1)/sqrt(2)`
when `x=+(1)/sqrt(2),y=(e^(-1))/(2)=(1)/sqrt(e )`
Thus the points of inflection are `(+1)/sqrt(2),(1)/sqrt(e)`