Determine the intervals where f(x)=e^-x^2/2 is increasing and decreasing

Answer 1

f(x) is increasing when f'(x)>0

ln(f)=-x^2/2 * e^(-x^2/2)

take the derivative.
f'/f(x)=-e^(-x^2/2)( -x)=xe^ ( )

then f'=xe^ ( ) * e^( )= xe^(-x^2)

check that.
so when x>0, f(x) is increasing.