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mimmax.wxmx - Calcula e classifica os pontos críticos de f

(%i1) kill(all);
\[\tag{%o0} \mathit{done}\]
(%i1) f:x^3+3·x·y^2−15·x−12·y; /· introduza aqui a função ·/
\[\tag{f}3 x\, {{y}^{2}}-12 y+{{x}^{3}}-15 x\]
(%i4) fx:diff(f,x)$ fy:diff(f,y)$ display(fx,fy)$
\[\mathit{fx}=3 {{y}^{2}}+3 {{x}^{2}}-15\mathit{fy}=6 x y-12\]
(%i5) sol:algsys([fx=0, fy=0], [x,y]);
\[\tag{sol}[[x=2,y=1],[x=1,y=2],[x=-1,y=-2],[x=-2,y=-1]]\]
(%i6) n:length(sol);
\[\tag{n}4\]
(%i7) for i:1 thru n do(
P[i]:subst(sol[i],[x,y]),
display(P[i])          
);
\[\mbox{}\\\mbox{ARRSTORE: use\_ fast\_ arrays=false; allocate a new property hash table for |\$ p|}{P_1}=[2,1]\]
(%i9) define(fxx(x,y),diff(fx,x)); define(D(x,y),diff(fx,y)^2−diff(fx,x)·diff(fy,y));
\[{P_2}=[1,2]{P_3}=[-1,-2]{P_4}=[-2,-1]\] \[\tag{%o7} \mathit{done}\] \[\tag{%o8} \operatorname{fxx}\left( x,y\right) :=6 x\] \[\tag{%o9} \operatorname{D}\left( x,y\right) :=36 {{y}^{2}}-36 {{x}^{2}}\]
(%i11) for i:1 thru n do(
D[i]:D(P[i][1],P[i][2]),fxx[i]:fxx(P[i][1],P[i][2]),
disp("−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−"),     
if D[i]>0 then display([P[i],D[i]])  else display([P[i],D[i],fxx[i]]),
if D[i]=0 then disp("indeterminado")
              else if D[i]>0 then print(P[i],"é ponto de sela")
                                  else if fxx[i]>0 then print(P[i], "é ponto de mínimo local")
                                                        else print(P[i],"é ponto de máximo local")
)$
disp("−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−")$
\[\mbox{}\\\mbox{ARRSTORE: use\_ fast\_ arrays=false; allocate a new property hash table for |\$ d|}\mbox{}\\\mbox{ARRSTORE: use\_ fast\_ arrays=false; allocate a new property hash table for \$ FXX}\mbox{}\\-----------------------------------------------[{P_1},{D_1},{{\mathit{fxx}}_1}]=[[2,1],-108,12][2,1] é ponto de mínimo local \mbox{}\\-----------------------------------------------[{P_2},{D_2}]=[[1,2],108][1,2] é ponto de sela \mbox{}\\-----------------------------------------------[{P_3},{D_3}]=[[-1,-2],108][-1,-2] é ponto de sela \mbox{}\\-----------------------------------------------[{P_4},{D_4},{{\mathit{fxx}}_4}]=[[-2,-1],-108,-12][-2,-1] é ponto de máximo local \mbox{}\\-----------------------------------------------\]
Created with wxMaxima.