Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/189



Consider the quantity Q defined by the equation

where in general all we know about $$x_1$$ is that it lies between a and b.

The Theorem of Mean Value interpreted Geometrically. Let the curve in the figure be the locus of



Take OC = a and OD = b; then $$f(a) = CA$$ and $$f(b) = DB$$, giving $$AE = b - a$$ and $$EB =f(b) - f(a)$$.

Therefore the slope of the chord AB is