Question

The function f(x) = 4 - 3x+3x² - x³ is

A. decreasing on R

B. increasing on R

C. strictly decreasing on R

D. strictly increasing on R

Answer 1

f(x) = -x³+3x² - 3x+4.

f’(x) = -3x²+6x - 3

f’(x) = -3(x² - 2x+1)

f’(x) = -3(x -1)²

As f’(x) has –ve sign before 3

⇒ f’(x) is decreasing over R.