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NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

Let a continuous and differentiable function f x is such that f x and d d x f x have opposite signs everywhere. Then,

Options

  1. Af ′ x is always increasing
  2. Bf x is always increasing
  3. Cf x is non-decreasing
  4. Df x is decreasing

Correct answer

D. f x is decreasing

Step-by-step solution

f x = f x : f x ≥ 0 - f x : f x < 0 d d x f x = f ' x : f x ≥ 0 - f ' x : f x < 0 As f x and f ′ x have opposite signs, then d d x f x is negative everywhere, hence f x is a decreasing function.

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