Mean Value Theorem (Calculus)

The Mean Value Theorem states that $x_1<c<x_2$ and $f^{\prime }\left(c\right)=0$, meaning that there is a critical point in that range, for a function $f\left(x\right)$ if the following conditions are met^[1]:

• It is continuous on the close interval $[x_1,x_2]$.
• It is differentiable on the open interval $(x_1,x_2)$.
• $f\left(x_1\right)=f\left(x_2\right)$

1. The Mean Value Theorem (Section 4.7) via Paul’s Online Notes ↩