Derivative Definition

Move the "a" slider to view the tangent line at various points on the graph of

. Tick the "secant line" box and move the "h" slider to view secant lines whose slopes approximate the slope of the tangent line. Notice that the orange secant line looks more and more like the blue tangent line as h approaches 0. Tick the "show slopes" box to view formulas for the slope of the secant line (i.e, the difference quotient) and the slope of the tangent line (i.e., the derivative).