Up: Some Special Cases
Tangents and Calculus
Say we have a function f(x), and we want to define
analytically the line tangent to the graph at the point
(x,f(x)). Then we say define the
tangent line as the line passing through that point with slope equal to
the derivative at that point, namely
f(w)-f(x)
f'(x) = lim ---------.
w->x w-x
If we drew secant lines drawn from the point
(x,f(x)) to other points
(w,f(w)) which approach it along the curve, this
derivative would be precisely the limit of the slopes of those lines.
Up: Some Special Cases
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Created: Nov 30 1995 ---
Last modified: Thu Nov 30 15:11:26 1995