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The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].
Why it is called mean value theorem?
The reason it's called the “mean value theorem” is because the word “mean” is the same as the word “average”. In math symbols, it says: ... f(b) − f(a) Geometric Proof of MVT: Consider the graph of f(x).
What does the mean value theorem guarantee?
The mean value theorem guarantees, for a function f that's differentiable over an interval from a to b, that there exists a number c on that interval such that f ′ ( c ) f'(c) f′(c)f, prime, left parenthesis, c, right parenthesis is equal to the function's average rate of change over the interval.
