The Mean Value Theorem states that for a continuous, differentiable function over a given internval, there exists some point on the curve whose tangent line has a slope that equals the slope of the secant line that connects the starting and ending points of the interval.
For example, here we will find the point between the interval [-2,3] that meets the requirement of the Mean Value Theorem for the function: $f\left(x\right)={x}^{2}-3x-1$
Mean Value Theorem Functions