o:=x->0.0001;

a:=x->1/10000*x;

b:=x->1/30000*(x-4000)+4/10; expand(b(x));

c:=x->6/10;

oo:=x->piecewise([x<0,0],[x>=0 and x<2000,o(x)] ):

aa:=x->piecewise([x<0,0],[x>=2000 and x<4000,a(x)] ):

bb:=x->piecewise([x<0,0],[x>=4000 and x<10000,b(x)] ):

cc:=x->piecewise([x<0,0],[x>=10000 ,c(x)] ):

plotfunc2d(aa(x),bb(x),cc(x),oo(x),x=0..16000, LineWidth=0.8,

            LegendVisible=FALSE, GridVisible=TRUE,

            ViewingBoxYRange=0..0.6)

 

 

 

a:=x->1/10000*x;

b:=x->1/30000*(x-4000)+4/10; expand(b(x));

c:=6/10;

g:=x->piecewise( [x<2000,0],[2000<=x and x<4000,a(x)],

                            [4000 <=x and x<10000,b(x)],

                            [x>10000,c(x)]);

g(x)

plotfunc2d(g(x),x=0..16000)

s:=x->int(g(x), x);

s(x)

 

plotfunc2d(s(x),x=0..16000)

A:=x->1/20000*x^2+ka;A(x);A(2000);

ka:=solve(A(2000)=0,ka)[1]

A(x), A(4000)

b(x);

B:=x->1/60000*x^2+4/15*x+kb; B(4000)

delete(kb);

kb:=solve(A(4000)=B(4000),kb)[1]

B(10000)

delete(kc)

C:=x->6/10*x+kc;

kc:=solve(C(10000)=B(10000),kc)[1];

plotfunc2d(A,B,C,x=0..16000)

s:=x->piecewise([x<2000,0],[x>=2000 and x < 4000,A(x)],

         [x>=4000and x<10000,B(x)],[x>=10000,C(x)])

plotfunc2d(s(x),x=0..16000)

s(x)

sg:=plot::Function2d(s(x),x=0..16000)

plot(sg)

AA:=x->piecewise([x<0,0],[x>=2000 and x<4000,A(x)] ):

BB:=x->piecewise([x<0,0],[x>=4000 and x<10000,B(x)] ):

CC:=x->piecewise([x<0,0],[x>=10000 ,C(x)] );

plotfunc2d(AA(x),BB(x),CC(x),oo(x),x=0..16000, LineWidth=0.8,

            LegendVisible=FALSE, GridVisible=TRUE )

sp:=plot::Function2d(0.6,x=0..16000):

plot(plot::Function2d(s(x)/x,x=0..16000),sp)