**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