Question

f(x) = (x+1)³(x - 3)³ is increasing in

A. (-∞, 1)

B. (-1, 3)

C. (3, ∞)

D. (1, ∞)

Answer 1

Answer is : D. (1, ∞)

Given:

⇒ f(x) = (x+1)³.(x - 3)³

⇒ f’(x) = 3(x+1)²(x - 3)³ + 3(x - 3)³ (x+1)³

Put f’(x) = 0

⇒ 3(x+1)²(x - 3)³ = -3(x - 3)²(x+1)³

⇒ x - 3 = -(x+1)

⇒ 2x = 2

⇒ x = 1

When x>1 the function is increasing.

x<1 function is decreasing.

So, f(x) is increasing in (1, ∞).