QUESTION $9$

If $P_3$ is the third Taylor polynomial for the function $f(x)=2xcosx$ centered at $c=,$ then $P_3(\frac{3}{2})=$

A$.\frac{3{}^3}{4}-\frac{3}{8}$

B$.\frac{3{}^3}{16}-\frac{3}{2}$

C$.\frac{3{}^2}{8}-\frac{3}{4}$

D$.\frac{3{}^3}{8}-3$

E$.\frac{3{}^2}{8}-3$