1) If f:R→ R is differentiable function such that f'(x) >2f(x) for all x ε R, and f(0)=1 then A) $f(x)\gt e^{2x}in (0,\infty)$ B) $f(x)\lt;e^{2x}in (0,\alpha)$ C) f(x) is increasing in $(0,\infty)$ D) f(x) decresing in $(0,\infty)$ Answer: Option A,CExplanation: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) >e2x Also as f'(x)>2f(x) $\therefore$ f'(x)>2c2x>0
