Let f(x) be a real-valued function and let P = (a, f(a)) be a point on the graph of f(x). Then the tangent line to the graph of f(x) at the point P is the line through P with slope m = lim_(x->a) (f(x) - f(a))/(x - a) (as long as this limit exists). Geometrically, the tangent line is the line that touches the graph of f(x) at the point P and has the same slope as the graph at that point.

derivative | function | graph of a function | limit of a function | secant line

average rate of change | instantaneous rate of change

Euclid | Pierre de Fermat | René Descartes | Isaac Newton | Gottfried Leibniz