Answer to Question #308088 in Calculus for Mbukushu

Question

Question 6 [2]

State the mean Value Theorem.

Answer 1

The theorem states that if $f$ is a continuous function on the closed interval $[a,b]$ and differentiable on the open interval $(a,b),$ then there exists a point $c$ in $(a,b)$ such that the tangent at $c$ is parallel to the secant line through the endpoints ${\displaystyle {\big (}a,f(a){\big )}}$ and ${\displaystyle {\big (}b,f(b){\big )}},$ that is,

${\displaystyle f'(c)={\frac {f(b)-f(a)}{b-a}}.}$