Q. 74

# Mark (√) against the correct answer in the following:

is increasing in

A. (-2, 0)

B. (0, 2)

C. (2, ∞)

D. (-∞, ∞)

Answer :

Given f(x) = x^{2}.e^{-x}

⇒ f’(x) = 2x. e^{-x} – x^{2} e^{-x}

⇒ Put f’(x) = 0

⇒ - (x^{2}– 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.

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