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) = limit((f(a+h)-f(a))/h,proc (h) options operator, arrow; 0 end proc)

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;

f := proc (x) options operator, arrow; 10*x-x^3+1 end proc

>    tandemo(f,-2);

[Maple Plot]

>