Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If f : R → R is a differentiable function such that f ′ (x) > 2f(x) for all x ∈ R, and f(0) = 1, then
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,c)
Sol. f'(x) – 2f(x) > 0
⇒ 
⇒ g(x) = f(x).e –2x is an increasing function.
for x > 0 , g(x) > g(0)
⇒ f(x).e –2x > 1 ⇒ f(x) > e 2x
Now f'(x) > 2f(x) > 2.e 2x
∴ f(x) is an increasing function
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