The degree $4$ Maclaurin polynomial that approximates a function $f$ is given by:

$P_4(x)=2+\frac{3}{4}{x}^2-5x^3+\frac{1}{2}{x}^4,$

Which of the following are true about $f?$

I. $f$ has a local minimum at $x=0.$

II$.f(0)=2$

III. $f$ is increasing at $x=0.$

a$)$NOne

b$)$ II only

c$)$ II and III

d$)$ III only