f(x) = [x(x - 3)]2 is increasing inA. (0, ∞)B. (-∞, 0)C. (1, 3)D.

1.	f(x) = [x(x - 3)]2 is increasing inA. (0, ∞)B. (-∞, 0)C. (1, 3)D. (0, 3/2) ∪ (3, ∞)
Answer» 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.

f(x) = [x(x - 3)]2 is increasing inA. (0, ∞)B. (-∞, 0)C. (1, 3)D. (0, 3/2) ∪ (3, ∞)

Answer»

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.