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CGP EDU Academic Team
Published on: August 13, 2026
f : [0, 4] → R is a differentiable function. Then prove that for some a, b ∈ (0, 4) , f 2 (4) – f 2 (0) = 8f ′
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Here f is a differentiable function then f is continuous function
So by L.M.V. theorem for any a ∈ (0, 4)
f ′ = 
...(1)
Again from mean value for any b ∈ (0, 4)
f(b) = 
...(2)
Now multiplying (1) and (2), we get
= f ′ · f(b)
⇒ f 2 (4) – f 2 (0) = 8f ′ · f(b)
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