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

Question

If f x is a differentiable function satisfying f ' x ≤ 4 ∀ x ∈ 0 , 4 and f 0 = 0 , then, f x = 18 has no solution in x ∈ 0 , 4, f x = 18 has more than 2 solutions in x ∈ 0 , 4, f x = 14 has no solution in x ∈ 0 , 4, f x = 20 has 2 solution in x ∈ 0 , 4

MARKS App · Accepted Answer

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

Search any question & find its solution

Looking for more such questions to practice?