# What is the difference between Mean value theorem, Average value and Intermediate value theorem?

See the explanation.

All three have to do with continuous functions on closed intervals.

The Mean Value Theorem is about differentiable functions and derivatives.

The Average Value Theorem is about continuous functions and integrals . The Intermediate Value theorem is about continuous functions.

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The Mean Value Theorem states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the interval where the instantaneous rate of change (derivative) equals the average rate of change (slope of the secant line).

The Average Value of a function on a closed interval is calculated by finding the mean of the function values over that interval. It represents the value that would give the same area under the curve if the function were constant at that value.

The Intermediate Value Theorem states that if a function is continuous on a closed interval, then it takes on every value between the function values at the endpoints of the interval.

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