The maximum value of $4\sin^2x+3\cos^2x+\sin\large\frac{x}{2}$$+\cos\large\frac{x}{2}$ is

Question

$$\begin{array}{1 1}(a)\;4+\sqrt 2&(b)\;3+\sqrt 2\\(c)\;9&(d)\;4\end{array}$$