Question

f(x) = x²e^-x is increasing in

A. (-2, 0)

B. (0, 2)

C. (2, ∞)

D. (-∞, ∞)

Answer 1

Answer is : B. (0, 2)

Given : f(x) = x².e^-x

⇒ f’(x) = 2x. e^-x – x² e^-x

⇒ Put f’(x) = 0

⇒ - (x²– 2x)e^-x = 0

⇒ x = 0 or x = 2.

Now as there is a -ve sign before f’(x)

When x > 2 the function is decreasing

x < 0 function is decreasing

But in the interval (0,2) the function is increasing.