Secant and Tangent lines
Drag B towards A. Notice that the secant line (green line) converges toward the tangent line (blue line).
Move A to a different place. Can you move A anywhere so that this doesn't work?
Try it with different functions.
Here are some suggestions:
f(x)=sin(x)
f(x)=x^(2/3)
f(x)=x^(1/3)
Pay particular attention to what happens to the secant line when A is at the origin.