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CGP EDU Academic Team
Published on: August 11, 2026
Let f(x) be differentiable function and g(x) be twice differentiable function. Zeros of f(x), g ′ (x) be a, b respectively (a < b). Show that there exists at least one root of equation f ′ (x) g ′ (x) + f(x) g ′′ (x) = 0 on (a, b).
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Let h(x) = f(x) g ′ (x)
h(a) = 0 = h(b)
By Rolle ’ s theorem on [a, b] h ′ (x) = 0, for at least one c ∈ (a, b).
⇒ f ′ g ′ + f(c) g ″ = 0
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