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If f x is a differentiable function satisfying f ' x ≤ 4   ∀ 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 no solution in x ∈ 0 , 4
  4. Df x = 20 has 2 solution 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 ≤ 4 ⇒ f t ≤ 4 t As t ∈ 0 , 4 ∴ f t ≤ 16

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