Q: $f\left(x\right)$ is a continuous and differentiable function defined in $[0,\infty)$. If $f\left(0\right)=1$ and $f'\left(x\right)>3f\left(x\right)\ $ $∀\ x\ \ge0$ then prove that $f\left(x\right)\ge e^{3x}\ ∀\ x\ \ge0$ Approach: Given $$f'\left(x\right)>3f\left(x\right)\ $$ Let $f\left(x\...