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Mean Value Theorem

Mean Value Theorem

A major theorem of calculus that relates values of a function to a value of its derivative. Essentially the theorem states that for a "nice" function, there is a tangent line parallel to any secant line.

 

Mean Value Theorem: if f is continuous on [a,b] and differentiable on (a,b), then f'(c) = (f(b) - f(a)) / (b - a)
Graph of y=f(x) showing secant line with slope (f(b)-f(a))/(b-a) and parallel tangent line with slope f'(c) at point (c,f(c)).

 

See also

Mean value theorem for integrals, continuous, differentiable, slope, Rolle's theorem