MATH 131, seciton 1 -- Calculus for Physical and Life Sciences
The derivative at a point -- Maple demo
September 27, 2004
In class today, we studied the derivative at a point:
f '(a) =
Geometrically, this corresponds to taking the limit
as h -> 0 of the slope of the line through (a, f(a))
and (a+h, f(a+h)) on the graph. In the limit,
we obtain the slope of the tangent line to y = f(x)
at x = a, provided that there is a single, well-defined
tangent line. Here is a Maple animation demo that
shows this process.
> | read "/home/fac/little/public_html/MATH131-132/tanlimit.map"; |
> | with(plots): |
> | f:=x->10*x-x^3+1; |
> | tandemo(f,-2); |
> |