Secant Line/Tangent Line

Here is the animation showing how the secant line turns into the tangent line as h -> 0.

Equivalently, how the limit of d(h) [the slope of the secant line] as h goes to 0 is the definition of the slope of the tangent line to P.

Note, in the animation we're starting with h=2 (so Q=(4,16) ) and letting h go to 0 from there.

As such, the point Q moves closer and closer to P.