Find the critical numbers

Question

x^2 e^(-4 x)

Answer 1

The Function is .

Apply derivative on each side.

               (Apply differentiation rule )

For Critical points f' (x) = 0.

As is not defined, we do not consider it.

2x (1 - x) = 0.

x = 0 or 1.

Substitute x =0 in f(x).

f(0) = 0.

Substitute x =1 in f(x).

Therefore the critical points are (0,0) and (1, 0.0183).