QJEEAdv17Mac9c5: JEE Advanced 2017 Mathematics - Class 12 JEEAdv17Mac9c5 Solution: f : R → R is a differentiable function such that f'(x) > 2f(x)…

Question

Verified Solution • 2025–26 Session moderate

f : R

\to

R is a differentiable function such that f'(x) > 2f(x) for all x

\in

R, and f(0) = 1 then

Accepted Answer

f^{'} (x) > 2 f (x)

\Rightarrow \frac{d y}{y} > 2 d x

\Rightarrow \int_{1}^{f (x)} \frac{d y}{y} > 2 \int_{0}^{x} d x

\ln (f (x)) > 2 x

∴

f (x) > e^{2 x}

Also, as

f^{'} (x) > 2 f (x)

∴

f^{'} (x) > 2 c^{2 x} > 0

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