i plugged in zero in the derivative, and i got: e^-0*0e^-0 = 0 1*0= 0 so is the critical point zero then???
I got f'(x) = x(-e^-x) + e^-x) = e^-x(-x+1) setting this = 0 gives x=1 if x=1 f(1) = 1(e^-1) = 1/e so we have a critical point at (1,1/e)
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