TS EAMCET 4 May 2018 Shift 2 Solved Paper

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=

1

e2