Let  $f\left(x\right)$ be a function defined by  $f\left(x\right)=\underset{0}{\overset{3\pi /4}{\int }}|x\cos t-3\sin t+\sqrt{2}x|\left(\frac{1+\sqrt{2}\cos t}{{(\cos t+\sqrt{2})}^3}\right)dt$ where  $x$ is any real number, then which of the following options is/are true ?

$f\left(x\right)$ is continuous for all  $x$  but non-differentiable at two values of  $x$

Minimum value of  $f\left(x\right)\text{is}\frac{3}{2}forx\in R$

$f\left(x\right)$ is continuous and differentiable every where 

Minimum value of  $f\left(x\right)\text{is}\frac{3}{4}forx\in R$