code for diagram
>
f:=x->.13*(x^2+2*sin(x*7)):
P1a:=plot(f(x), x=2..4,thickness=3,title=`A(u+Delta u) -
A(u)`,titlefont=[TIMES,BOLD,22]):
deltaarea:=[[3.2,0],seq([3.2+i*.4/20,f(3.2+i*.4/20)],
i=0..20),[3.6,0],[3.2,0]]:
plotdeltaarea:=plots[polygonplot](deltaarea,style=patch,
color=tan):
A1:=labeledarrow([4.2,-.4],[3.6,0],[3,4,5],`u + delta u`,
[-.5,-.1],14,blue):
A2:=labeledarrow([3.0,-.4],[3.2,0],[3,4,5],`u`,
[-.30,-.1],14,blue):
A4:=labeledarrow([4.5,0],[4.5,f(3.2)],[2,4,2],`f(u)`,
[0,.3],14,blue):
A5:=labeledarrow([4.5,f(3.2)],[4.5,0],[2,4,2],``,
[0,.3],14,blue):
txt2:=plots[textplot]({[1.8,.2,`a`],[4.2,.2,`b`],
[3,f(3)+.3,`y=f(u)`]},font=[TIMES,BOLD,16]):
dtln:=plot([[3.1,f(3.2)],[4.7,f(3.2)]],color=blue,
thickness=3,linestyle=3):
plots[display]([P1a,txt2,lines,dtln,plotdeltaarea,A1,
A2,A4,A5],scaling=constrained,xtickmarks=[],
ytickmarks=[],view=[1..5,-2..f(4)+1] );