If f : R → R is a differentiable function such that f ′ (x)…

Maths Differentiation and Applications of Derivatives JEE (Advanced) / IIT - JEE Problems ( Previous Years ) Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If f : R → R is a differentiable function such that f ′ (x) > 2f(x) for all x ∈ R, and f(0) = 1, the

f(x) > e 2x in (0, ∞ )

f ′ (x) < e 2x in (0, ∞ )

f(x) is increasing in (0, ∞ )

f(x) is decreasing in (0, ∞ )

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a,c)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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