Relations Functions

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

  1. (-∞,1/3] ; 3x2 - 2x + 1
  2. [2,∞) ; 2x3 - 3x2 -12x + 6
  3. (-∞,∞) ; x3 - 3x2 + 3x + 3
  4. (-∞,-4] ; x3 + 6x2 + 6

Answer

f(x) = x3 + 6x2 + 6

f'(x) = 3x2 + 12x = 3x(x+4)

f'(x) > 0, x < -4 U x > 0

The interval x < -4 i.e (-∞, -4] matched correctly.

The correct option is A.