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CGP EDU Academic Team
Published on: August 13, 2026
Given a function f : [0, 4] ⎯→ R is differentiable, then for some a, b ∈ (0, 4) [f(4)] 2 – [f(0)] 2 =
Text Solution
Verified by ExpertsThe correct answer is:
A
Since f(x) is differentiable in [0, 4], using Lagrange's Mean Value Theorem.
f ′ = 
, b ∈ (0, 4) …(1)
Now, {f(4) 2 – {f(0)} 2 = 
{f(4) + f(0)}
= 4f ′ {f(4) + f(0)}… (2)
Also, from Intermediate Mean Value Theorem,
= f(a) for a ∈ (0, 4).
Hence, from (2) [f(4) 2 ] – [f(0)] 2 = 8f ′ f(a).
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