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CGP EDU Academic Team
Published on: August 14, 2026
If f and g are differentiable functions in [0, 1] satisfying f(0) = 2 = g(a), g(0) = 0 and f(a) = 6, then for some c ∈ ]0, 1[ :
Text Solution
Verified by ExpertsThe correct answer is:
B
Consider f(x) – 2g(x) = h(x)
Then, h(x) is continuous and differentiable in [0, 1]
Also h(0) = 2 & h(a) = 2
Hence h(x) satisfies conditions of Rolles Theorem in (0, 1)
Thus, There exist a 'c' such that h' = 0 where c ∈ (0, 1)
⇒ f' = 2g'
f(x) – 2g(x) = h(x)
h(0) = 2 o h(a) = 2
= 0 ¡ c ∈ (0, 1)
⇒ f' = 2g'
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