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.

Let f(x) be a function. Then the graph of f(x), sometimes called a curve, is the set of points (x, f(x)) for all x in the domain of f(x).

concepts involved | derivative | function | graph of a function related concepts | average rate of change | instantaneous rate of change

concepts involved | domain of a function | function | set related concepts | secant line | tangent line

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

Gottfried Leibniz | Leonhard Euler