In this worksheet we will examine animations of secant lines. This feature is available through the secant lines button on the Calculus Menu of MenuMaple.

Example One

Enter cos(x/3) as an expression named f.

> f:=cos(x/3);

On the Calculus Menu select secant lines.. . and then select animation of secants . Use f as the expression and 0 as the value of a. Once the initial graph is drawn ask your instructor for help getting the animation to start.  Note that the red line is the right secant while the blue line is the left secant.

> with(math191):

> gseclines(f,x=0);

Do the secant lines appear to be approaching a common line? Is f differentiable at a=0?

Example Two

Enter piecewise(x<0,x^2,x>=0,x^3) as g

> g:=piecewise(x<0,x^2,x>=0,x^3);

Produce an animation for the secants for g through a=0.

> gseclines(g,x=0);

Do these secants appear to approach a common line? Is g differentiable at a=0?

Example Three

Enter piecewise(x<2,x^2,x>=2,8-x^2) as h.

> h:=piecewise(x<2,x^2,x>=2,8-x^2);

Produce an animation of the secants for h through a=2.

> gseclines(h,x=2);

Do the secant lines approach a common line? Is h differentiable at a=2?

Let's examine the corner on the graph of h more closely. Make a graph of h with x between 1.9999 and 2.0001.

> plot(h,x=1.9999..2.0001);

Now make a graph for h with x between 1.99999 and 2.00001

> plot(h,x=1.99999..2.00001);

If you could continue making graphs for h over a smaller and smaller interval about 2, do think you can get rid of the corner?

>

Dan Symancyk February 1998