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NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

If f x is a differentiable function satisfying f ' x ≤ 2 ∀ x ∈ 0 , 4 and f 0 = 0 , then

Options

  1. Af x = 18 has no solution in x ∈ 0,4
  2. Bf x = 18 has more than 2 solutions in x ∈ 0,4
  3. Cf x = 14 has 3 solutions in x ∈ 0,4
  4. Df x = 20 has 2 solutions in x ∈ 0,4

Correct answer

A. f x = 18 has no solution in x ∈ 0,4

Step-by-step solution

Applying LMVT in x ∈ 0 , t for f x , we get, f ' c = f t − f 0 t − 0 ⇒ f ' c = f t t ≤ 2 ⇒ f t ≤ 2 t as t ∈ 0 , 4 ∴ f t ≤ 8 ⇒ - 8 ≤ f t ≤ 8

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