Consider the equation, y=x2.e−2x,x>0. Differentiate above w.r.t x ,
dy
dx
=x2(−2)e−2x+e−2x(2x) For maxima, the first derivative will be equal to zero. 2xe−2x(1−x)=0 x=0,1 This implies minima at x = 0 and maxima at x = 1. So, yx=1(1)2e−2=