Increasing and Decreasing Functions

The function is increasing in the inetrval (0,2).

So, d is the correct option.

To get the solution following are the steps required:

y = x² e^-x

y' = 2x e^-x - x²e^-x

    = x e^-x (2 - x)

For turning points, y' = 0

⇒ x = 0, 2,

for x = 0      y' < 0

for x = 2      y' > 0

So, in the interval the function y = x² e^-x is an incerasing function.

Similarly you can also deduce that in interval (-, 0) and (2,) the function is decreasing.