structural:summarization, information:highlighting, structural:expansion, linguistic:translation
Intuitive description

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. If k is known, the equation of the tangent line can be found in the point-slope form: