For what choice of `a` and `b` is the function `f(x)={x^2\ \ \ ,\ \ \ xlt=c a x+b\ \ \ ,\ \ \ x > c` is differentiable at `x=c` .

Explanation

To determine the values of \( a \) and \( b \) for which the function

\[
f(x) =
\begin{cases}
x^2 & \text{if } x < c \\
ax + b & \text{if } x \geq c
\end{cases}
...