## Difference Quotient

is called [5] the mean (or average) value of the derivative of * f* over the interval [* a* , * b* ]. This name is justified by the mean value theorem , which states that for a differentiable function * f* , its derivative * f′* reaches its mean value at some point in the interval. [5] Geometrically, this difference quotient measures the slope of the secant line passing through the points with coordinates (* a* , * f* (* a* )) and (* b* , * f* (* b* )). [10]