f(x) = x2e-x is increasing inA. (-2, 0)B. (0, 2)C. (2, ∞)D. (-∞, �

1.	f(x) = x2e-x is increasing inA. (-2, 0)B. (0, 2)C. (2, ∞)D. (-∞, ∞)
Answer» 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.

f(x) = x2e-x is increasing inA. (-2, 0)B. (0, 2)C. (2, ∞)D. (-∞, ∞)

Answer»

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.