I am trying to do define the Mean Value theorem. I am haveing trouble explaining exactly what this theorem is telling me. Can someone help me? Thank You
Suppose that $\displaystyle f$ satisfies the conditions of the mean value theorem on $\displaystyle [a,b]$, then there is a point $\displaystyle c \in \left( {a,b} \right)$ such that the tangent at $\displaystyle \left( {c,f(c)} \right)$ is parallel to the secant determined by $\displaystyle \left( {a,f(a)} \right)\,\& \,\left( {b,f(b)} \right)$.