Use this mean value theorem calculator to quickly find the average rate of change over a specified interval for a given function.

# Mean Value Theorem Calculator

Use this simple calculator to find the average rate of change of a function in a given interval using the Mean Value Theorem.

## How to Use the Calculator

To use this calculator, input your function expression in the **f(x):** field using the variable *x* and typical arithmetic symbols. For example, input “3*x^2 – 2*x + 1” without quotes. Then, provide your interval start in the **a:** field and interval end in the **b:** field, and click the **Calculate** button.

## How the Calculator Works

The calculator uses the Mean Value Theorem formula, which states that for any function that is continuous on *[a, b]* and differentiable on *(a, b)*, there exists a point *c* in *(a, b)* such that *f'(c) = (f(b) – f(a)) / (b – a)*. In this calculator, we compute the average rate of change of the function over the interval *[a, b]* which corresponds to *f'(c)*.

## Limitations

This calculator assumes the function provided is correctly formatted and mathematically valid on the interval specified. It doesn’t handle functions that involve transcendental operations (like trigonometric functions), and does not validate whether the function is differentiable or continuous over the interval. For functions involving powers, use the caret symbol (^), such as “x^2” for “x squared”.