For what value of $a$ and $b$ is the function $f(x) = \begin{cases} x^2 ,& x \leq c \\ ax+b , & x> c \end{cases} $ is differentiable at $x=c$

Question

$(A)\; a = \frac{c}{2} , b = c^2$
$(B)\; a = 2c , b = c^2$
$(C)\; a= 2c, b = \frac{c}{2}$
$(D)\; a = 2c, b = -c^2$