Question

Let y = x²e^-x. Then the interval in which y increases with respect to x is

(A) (−∞, ∞)

(B) (2, 0)

(C) (2, ∞)

(D) (0,2)

Answer 1

Answer is (D) (0, 2)

We know that

dy/dx = -1/e^x(x(x - 2) is positive when x(x - 2) is negative, that is, x lies in the interval (0, 2). An exponential function, as we know, is always positive.