code for table

> f:='f':
M:=matrix([[x, -1.0, -.8, -.6, -.4, -.2, 0, .2, .4, .6, .8, 1.0], [`f`*`'`(x), .3, .4, .5, .6, 1.0, infinity, 1.0, .6, .5, .4, .3]]):

> convert(M,array);

> ptsneg:=seq([M[1,i],M[2,i]],i=2..6):
ptspos:=seq([M[1,i],M[2,i]],i=8..12) :

> p2:=plot({ptspos},style=line,scaling=constrained,color=blue,thickness=3):

> p1:=plot({ptsneg},style=line,scaling=constrained,color=blue,thickness=3):

> plots[display]( {grph,gp,p1,p2},titlefont=[TIMES,BOLD,14],title=`f(x) and graphical approx. of f'(x)` );

>