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    Tangent Map

    Alternate names

    map | mapping

    Results

    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.

    A function f is a rule that assigns to each element x in a set D (called the domain of f) exactly one element, called f(x), in a set C (called the codomain of f).

    Details

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

    concepts involved | set | domain of a function | codomain of a function related concepts | range of a function

    Associated people

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

    Gottfried Leibniz | Leonhard Euler

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