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.