Science:Math Exam Resources/Courses/MATH110/April 2014/Question 02 (c)/Solution 1

• Rolle’s Theorem: Let $f$ be a continuous function on $[a,b]$, differentiable on $(a,b)$, and satisfies $f(a)=f(b)$. Then there exists a point $c\in (a,b)$ such that $f'(c)=0$.
• MVT: Let $f$ be a continuous function on $[a,b]$ and differentiable on $(a,b)$. Then there exists a point $c\in (a,b)$ such that $f'(c)={\frac {f(b)-f(a)}{b-a}}$.