Application of Derivatives · Class 12 · CBSE · Science Mathematics

For the function f(x) = x³ − 12x + 5, the intervals on which f is increasing are:

Practice question from Application of Derivatives (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-F80671

For the function f(x) = x³ − 12x + 5, the intervals on which f is increasing are:

  1. A.(-∞, -2) and (2, ∞)Correct answer
  2. B.(-2, 2)
  3. C.(-∞, 2)
  4. D.(-2, ∞)

Solution

We have f′(x)=3x2−12=3(x−2)(x+2)f'(x)=3x^2-12=3(x-2)(x+2). This derivative is positive for x<−2x<-2 and x>2x>2, so the function is increasing on (−∞,−2)(-∞,-2) and (2,∞)(2,∞).

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