We have that \(\underset{h\rightarrow 0}{lim}\frac{f(c+h)-f(c)}{h}\) [the limit of the slope of the secant line] 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.