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