Secants to Tangents -- an animation of http://www.math.uakron.edu/~dpstory/tutorial/demos/tangent.pdf

MAT329
Andy Long, Spring, 2016.

Manipulate[
f[x_]:=5-(x-1)^2;
a=1.5;
m=(f[b]-f[a])/(b-a);
Plot[{f[x],m(x-a)+f[a]},{x,0,5},PlotRange->{0,7},PlotLabel->{"b=",b,"and m=",m}]
,{b,-1,3} 
]