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CGP EDU Academic Team
Published on: August 13, 2026
Let f : R → (0, ∞ ) and g : R → R be twice differentiable functions such that f " and g" are continuous functions on R. Suppose f '(2) = g(2) = 0, f "(2) ≠ 0 and g'(2) ≠ 0, If 
= 1, then
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,d) 
Indeterminant form as f'(2) = 0, g(2) = 0 Using L.H.
= 
= 
⇒ f"(2) = f(2)
and f'(2) = 0 & range of f(x) ∈ (0, ∞ )
so f"(2) = f(2) = +ve so f(x) has point of minima at x = 2
and f(2) = f"(2) so f(x) = f"(x) have atleast one solution in x ∈ R
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