Write $f(x)-f(a) = \frac{f(x)-f(a)}{x-a} \cdot (x-a)$ and take the limit

Write $f(x) = f'(a)(x-a)$ and substitute $x=a$

Use L'Hôpital's Rule on $\lim_{x\to a}f(x)$

Apply the Mean Value Theorem directly