Graphically, find the tangent line to the graph of the function

at the point **(0.5, 0.0625)** as the limit of secant lines.

We have two visualizations generated by **Maple**. The first is an
animation:

[Press here to see animation again!]

This was generated using the following code:

> f:=x->x^4;

> P := plot(f(x),x=-1.5..1.5,y=-2..4,color=red):

> Q := animate(((f(0.5+2^(-t))-f(0.5))/2^(-t)) * (x-0.5) + f(0.5), x=-1.5..1.5, t=0..10, frames=20, color=blue):

> display(P,Q);

The second shows all of the secant lines at once:

This was generated using the following code:

> f:=x->x^4;

> P := plot(f(x),x=-1.5..1.5,y=-2..4,color=red):

> A :=seq(plot(((f(0.5+2^(-i)) - f(0.5))/2^(-i)) * (x-0.5) + f(0.5), x=-1.5..1.5, color=blue), i=0..10):

> display(P,A);