Question

Let f(x) = `inte^x (x - 1)(x - 2)dx,` then f(x) decreases in the interval ______

Options

• (-∞, -2)

• (-2, -1)

• (1, 2)

• (2, ∞)

Answer 1

Let f(x) = `inte^x (x - 1)(x - 2)dx,` then f(x) decreases in the interval (1, 2).

Explanation:

f(x) = `inte^x (x - 1)(x - 2)dx`

⇒ f'(x) = e^x(x - 1)(x - 2) 

For f(x) to be decreasing, f'(x) < 0

⇒ e^x(x - 1)(x - 2) < 0

⇒ (x - 1) (x - 2) < 0

⇒ x ∈ (1, 2)