[Calculus] Quick Review for Tutorial 6

1. Definition of differentiation
We say $f$ is differentiate at $c$ if $lim_{x\rightarrow c} {f(x)-f(c) \over x-c}$ exists.

2. Mean Value Theorem
Suppose that a function is continuous on $[a,b]$ and differentiable on $(a,b)$. Then there exists c in $(a,b)$ such that

$$f\prime(c)={f(b)-f(a) \over b-a}.$$

3. Rolle’s theorem
Suppose that a function is continuous on $[a,b]$ and differentiable on $(a,b)$ and it satisfies $f(a)=f(b)$. Then there exists c in $(a,b)$ such that $f\prime(c)=0.$