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JEE Main20208 Jan 2020Evening ShiftMathematicsContinuity and DifferentiabilityActual

Let S , be the set of all functions f : 0 , 1 → R , which are continuous on 0 , 1 , and differentiable on 0 , 1 . Then for every f in S , there exists c ∈ 0 , 1 , depending on f , such that.

Options

  1. Af c - f 1 < 1 - c f ' c
  2. Bf 1 - f c 1 - c = f ' c
  3. Cf c + f 1 < 1 + c f ' c
  4. Df c - f 1 < f ' c

Correct answer

B. f 1 - f c 1 - c = f ' c

Step-by-step solution

Let us consider f x , a constant function, as constant functions are continuous and differentiable everywhere. Then, f 1 = f c   &   f ' c = 0 So, f 1 - f c 1 - c = f ' c = 0 .

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