Let f(x)=e^{-\frac{1}{x^{2}}}+\int_{0}^{\frac{\pi x}{2}} \sqrt{1+\sin t} d t \forall x \in(0, \infty) then-

f' exists and is continuous \forall x \in(0, \infty)

f" exists \forall x \in(0, \infty)

There exists \alpha>0 such that |f(x)|>| {f}^{'}( {x})| \forall x \in(\alpha, \infty)