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If f:R→ R is differentiable function such that f'(x) >2f(x) for all x ε R, and f(0)=1 then

$f(x)\gt e^{2x}in (0,\infty)$

$f(x)\lt;e^{2x}in (0,\alpha)$

C) f(x) is increasing in

$(0,\infty)$

D) f(x) decresing in

$(0,\infty)$

Option A,C

f'(x) >2f(x)

$\Rightarrow$ $\frac{dy}{y}>2dx$

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

$ln(f(x))>2x$

$\therefore$ f(x) >e^2x

Also as f'(x)>2f(x)

$\therefore$ f'(x)>2c^2x>0

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