Question

f(x) = [x(x - 3)]² is increasing in

A. (0, ∞)

B. (-∞, 0)

C. (1, 3)

D. (0, 3/2) ∪ (3, ∞)

Answer 1

Answer is : D. (0, 3/2) ∪ (3, ∞)

⇒ f(x) = [x(x - 3)]²

⇒ f'(x) = 2[x(x - 3)] = 0

⇒ x = 3 and x = 3/2

When x > 3/2 the function is increasing

x < 3 function is increasing.

⇒ (0, 3/2) ∪ (3, ∞) Function is increasing.