 Suppose that a curve is given as the graph of a function, "y" = "f"("x").To find the tangent line at the point "p" = ("a", "f"("a")), consider another nearby point "q" = ("a" + "h", "f"("a" + "h")) on the curve.The slope of the secant line passing through "p" and "q" is equal to the difference quotient

As the point "q" approaches "p", which corresponds to making "h" smaller and smaller, the difference quotient should approach a certain limiting value "k", which is the slope of the tangent line at the point "p".