> restart:
> Digits:=30:
> allvalues_:=true:
> f:=x1*cos(x1)+2*x2*x3-3*x3+4*x3*x4;
> # All
> sys:=diff(f,x1),diff(f,x2),diff(f,x3),diff(f,x4):
> sol:=solve({sys},{x1,x2,x3,x4}):
> evalf(subs(sol,f));
> # One fixed
> g:=subs(x1=-3,f):
> sys:=diff(g,x2),diff(g,x3),diff(g,x4):
> sol:=solve({sys},{x2,x3,x4}):
> evalf(subs(sol,g));
> g:=subs(x1=5,f):
> sys:=diff(g,x2),diff(g,x3),diff(g,x4):
> sol:=solve({sys},{x2,x3,x4}):
> evalf(subs(sol,g));
> g:=subs(x2=-3,f):
> sys:=diff(g,x1),diff(g,x3),diff(g,x4):
> sol:=solve({sys},{x1,x3,x4}):
> evalf(subs(sol,g));
> g:=subs(x2=5,f):
> sys:=diff(g,x1),diff(g,x3),diff(g,x4):
> sol:=solve({sys},{x1,x3,x4}):
> evalf(subs(sol,g));
> g:=subs(x3=-3,f):
> sys:=diff(g,x1),diff(g,x2),diff(g,x4):
> sol:=solve({sys},{x1,x2,x4}):
> evalf(subs(sol,g));
> g:=subs(x3=5,f):
> sys:=diff(g,x1),diff(g,x2),diff(g,x4):
> sol:=solve({sys},{x1,x2,x4}):
> evalf(subs(sol,g));
> g:=subs(x4=-3,f):
> sys:=diff(g,x1),diff(g,x2),diff(g,x3):
> sol:=solve({sys},{x1,x2,x3}):
> evalf(subs(sol,g));
> g:=subs(x4=5,f):
> sys:=diff(g,x1),diff(g,x2),diff(g,x3):
> sol:=solve({sys},{x1,x2,x3}):
> evalf(subs(sol,g));
> # Two fixed
> # x1,x2
> g:=subs(x1=-3,x2=-3,f):
> sys:=diff(g,x3),diff(g,x4):
> sol:=solve({sys},{x3,x4}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=-3,f):
> sys:=diff(g,x3),diff(g,x4):
> sol:=solve({sys},{x3,x4}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x2=5,f):
> sys:=diff(g,x3),diff(g,x4):
> sol:=solve({sys},{x3,x4}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=5,f):
> sys:=diff(g,x3),diff(g,x4):
> sol:=solve({sys},{x3,x4}):
> evalf(subs(sol,g));
> # x1,x3
> g:=subs(x1=-3,x3=-3,f):
> sys:=diff(g,x2),diff(g,x4):
> sol:=solve({sys},{x2,x4}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x3=-3,f):
> sys:=diff(g,x2),diff(g,x4):
> sol:=solve({sys},{x2,x4}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x3=5,f):
> sys:=diff(g,x2),diff(g,x4):
> sol:=solve({sys},{x2,x4}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x3=5,f):
> sys:=diff(g,x2),diff(g,x4):
> sol:=solve({sys},{x2,x4}):
> evalf(subs(sol,g));
> # x1,x4
> g:=subs(x1=-3,x4=-3,f):
> sys:=diff(g,x2),diff(g,x3):
> sol:=solve({sys},{x2,x3}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x4=-3,f):
> sys:=diff(g,x2),diff(g,x3):
> sol:=solve({sys},{x2,x3}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x4=5,f):
> sys:=diff(g,x2),diff(g,x3):
> sol:=solve({sys},{x2,x3}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x4=5,f):
> sys:=diff(g,x2),diff(g,x3):
> sol:=solve({sys},{x2,x3}):
> evalf(subs(sol,g));
> # x2,x3
> g:=subs(x2=-3,x3=-3,f):
> sys:=diff(g,x1),diff(g,x4):
> sol:=solve({sys},{x1,x4}):
> evalf(subs(sol,g));
> g:=subs(x2=5,x3=-3,f):
> sys:=diff(g,x1),diff(g,x4):
> sol:=solve({sys},{x1,x4}):
> evalf(subs(sol,g));
> g:=subs(x2=-3,x3=5,f):
> sys:=diff(g,x1),diff(g,x4):
> sol:=solve({sys},{x1,x4}):
> evalf(subs(sol,g));
> g:=subs(x2=5,x3=5,f):
> sys:=diff(g,x1),diff(g,x4):
> sol:=solve({sys},{x1,x4}):
> evalf(subs(sol,g));
> # x2,x4
> g:=subs(x2=-3,x4=-3,f):
> sys:=diff(g,x1),diff(g,x3):
> sol:=solve({sys},{x1,x3}):
> evalf(subs(sol,g));
> g:=subs(x2=5,x4=-3,f):
> sys:=diff(g,x1),diff(g,x3):
> sol:=solve({sys},{x1,x3}):
> evalf(subs(sol,g));
> g:=subs(x2=-3,x4=5,f):
> sys:=diff(g,x1),diff(g,x3):
> sol:=solve({sys},{x1,x3}):
> evalf(subs(sol,g));
> g:=subs(x2=5,x4=5,f):
> sys:=diff(g,x1),diff(g,x3):
> sol:=solve({sys},{x1,x3}):
> evalf(subs(sol,g));
> # x3,x4
> g:=subs(x3=-3,x4=-3,f):
> sys:=diff(g,x1),diff(g,x2):
> sol:=solve({sys},{x1,x2}):
> evalf(subs(sol,g));
> g:=subs(x3=5,x4=-3,f):
> sys:=diff(g,x1),diff(g,x2):
> sol:=solve({sys},{x1,x2}):
> evalf(subs(sol,g));
> g:=subs(x3=-3,x4=5,f):
> sys:=diff(g,x1),diff(g,x2):
> sol:=solve({sys},{x1,x2}):
> evalf(subs(sol,g));
> g:=subs(x3=5,x4=5,f):
> sys:=diff(g,x1),diff(g,x2):
> sol:=solve({sys},{x1,x2}):
> evalf(subs(sol,g));
> # Three fixed
> # x1,x2,x3
> g:=subs(x1=-3,x2=-3,x3=-3,f):
> sys:=diff(g,x4):
> sol:=solve({sys},{x4}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=-3,x3=-3,f):
> sys:=diff(g,x4):
> sol:=solve({sys},{x4}):
> evalf(subs(sol,g)):
> g:=subs(x1=-3,x2=5,x3=-3,f):
> sys:=diff(g,x4):
> sol:=solve({sys},{x4}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=5,x3=-3,f):
> sys:=diff(g,x4):
> sol:=solve({sys},{x4}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x2=-3,x3=5,f):
> sys:=diff(g,x4):
> sol:=solve({sys},{x4}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=-3,x3=5,f):
> sys:=diff(g,x4):
> sol:=solve({sys},{x4}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x2=5,x3=5,f):
> sys:=diff(g,x4):
> sol:=solve({sys},{x4}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=5,x3=5,f):
> sys:=diff(g,x4):
> sol:=solve({sys},{x4}):
> evalf(subs(sol,g));
> # x1,x2,x4
> g:=subs(x1=-3,x2=-3,x4=-3,f):
> sys:=diff(g,x3):
> sol:=solve({sys},{x3}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=-3,x4=-3,f):
> sys:=diff(g,x3):
> sol:=solve({sys},{x3}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x2=5,x4=-3,f):
> sys:=diff(g,x3):
> sol:=solve({sys},{x3}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=5,x4=-3,f):
> sys:=diff(g,x3):
> sol:=solve({sys},{x3}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x2=-3,x4=5,f):
> sys:=diff(g,x3):
> sol:=solve({sys},{x3}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=-3,x4=5,f):
> sys:=diff(g,x3):
> sol:=solve({sys},{x3}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x2=5,x4=5,f):
> sys:=diff(g,x3):
> sol:=solve({sys},{x3}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x2=5,x4=5,f):
> sys:=diff(g,x3):
> sol:=solve({sys},{x3}):
> evalf(subs(sol,g));
> # x1,x3,x4
> g:=subs(x1=-3,x3=-3,x4=-3,f):
> sys:=diff(g,x2):
> sol:=solve({sys},{x2}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x3=-3,x4=-3,f):
> sys:=diff(g,x2):
> sol:=solve({sys},{x2}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x3=5,x4=-3,f):
> sys:=diff(g,x2):
> sol:=solve({sys},{x2}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x3=5,x4=-3,f):
> sys:=diff(g,x2):
> sol:=solve({sys},{x2}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x3=-3,x4=5,f):
> sys:=diff(g,x2):
> sol:=solve({sys},{x2}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x3=-3,x4=5,f):
> sys:=diff(g,x2):
> sol:=solve({sys},{x2}):
> evalf(subs(sol,g));
> g:=subs(x1=-3,x3=5,x4=5,f):
> sys:=diff(g,x2):
> sol:=solve({sys},{x2}):
> evalf(subs(sol,g));
> g:=subs(x1=5,x3=5,x4=5,f):
> sys:=diff(g,x2):
> sol:=solve({sys},{x2}):
> evalf(subs(sol,g));
> # x2,x3,x4
> g:=subs(x2=-3,x3=-3,x4=-3,f):
> sys:=diff(g,x1):
> sol:=solve({sys},{x1}):
> evalf(subs(sol,g));
> g:=subs(x2=5,x3=-3,x4=-3,f):
> sys:=diff(g,x1):
> sol:=solve({sys},{x1}):
> evalf(subs(sol,g));
> print("-----");
> g:=subs(x2=-3,x3=5,x4=-3,f):
> sys:=diff(g,x1):
> sol:=eval(solve({sys},{x1}));
> evalf(subs(sol,g));
> g:=subs(x2=5,x3=5,x4=-3,f):
> sys:=diff(g,x1):
> sol:=solve({sys},{x1}):
> evalf(subs(sol,g));
> g:=subs(x2=-3,x3=-3,x4=5,f):
> sys:=diff(g,x1):
> sol:=solve({sys},{x1}):
> evalf(subs(sol,g));
> g:=subs(x2=5,x3=-3,x4=5,f):
> sys:=diff(g,x1):
> sol:=solve({sys},{x1}):
> evalf(subs(sol,g));
> g:=subs(x2=-3,x3=5,x4=5,f):
> sys:=diff(g,x1):
> sol:=solve({sys},{x1}):
> evalf(subs(sol,g));
> g:=subs(x2=5,x3=5,x4=5,f):
> sys:=diff(g,x1):
> sol:=solve({sys},{x1}):
> evalf(subs(sol,g));
> # x1,x2,x3,x4
> evalf(subs(x1=-3,x2=-3,x3=-3,x4=-3,f));
> evalf(subs(x1= 5,x2=-3,x3=-3,x4=-3,f));
> evalf(subs(x1=-3,x2= 5,x3=-3,x4=-3,f));
> evalf(subs(x1= 5,x2= 5,x3=-3,x4=-3,f));
> evalf(subs(x1=-3,x2=-3,x3= 5,x4=-3,f));
> evalf(subs(x1= 5,x2=-3,x3= 5,x4=-3,f));
> evalf(subs(x1=-3,x2= 5,x3= 5,x4=-3,f));
> evalf(subs(x1= 5,x2= 5,x3= 5,x4=-3,f));
> evalf(subs(x1=-3,x2=-3,x3=-3,x4= 5,f));
> evalf(subs(x1= 5,x2=-3,x3=-3,x4= 5,f));
> evalf(subs(x1=-3,x2= 5,x3=-3,x4= 5,f));
> evalf(subs(x1= 5,x2= 5,x3=-3,x4= 5,f));
> evalf(subs(x1=-3,x2=-3,x3= 5,x4= 5,f));
> evalf(subs(x1= 5,x2=-3,x3= 5,x4= 5,f));
> evalf(subs(x1=-3,x2= 5,x3= 5,x4= 5,f));
> evalf(subs(x1= 5,x2= 5,x3= 5,x4= 5,f));

              f := x1 cos(x1) + 2 x2 x3 - 3 x3 + 4 x3 x4


                  -0.561096338191045067540403753161


                   2.96997748980133637181471838419


                   1.41831092731613132233319585757


                  -0.561096338191045067540403753161


                  -0.561096338191045067540403753161


                   x1 cos(x1) - 6. x2 + 9. - 12. x4


                  x1 cos(x1) + 10. x2 - 15. + 20. x4


                  -0.561096338191045067540403753161


                  -0.561096338191045067540403753161


                   2.96997748980133637181471838419


                   1.41831092731613132233319585757


                   2.96997748980133637181471838419


                   1.41831092731613132233319585757


           11.9699774898013363718147183842 - 6. x2 - 12. x4


           10.4183109273161313223331958576 - 6. x2 - 12. x4


          -12.0300225101986636281852816158 + 10. x2 + 20. x4


          -13.5816890726838686776668041424 + 10. x2 + 20. x4


                   2.96997748980133637181471838419


                   1.41831092731613132233319585757


                   2.96997748980133637181471838419


                   1.41831092731613132233319585757


                      x1 cos(x1) + 27. - 12. x4


                      x1 cos(x1) - 21. - 12. x4


                      x1 cos(x1) - 45. + 20. x4


                      x1 cos(x1) + 35. + 20. x4


                         x1 cos(x1) - 21. x3


                          x1 cos(x1) - 5. x3


                         x1 cos(x1) + 11. x3


                         x1 cos(x1) + 27. x3


                       x1 cos(x1) - 6. x2 + 45.


                      x1 cos(x1) + 10. x2 - 75.


                       x1 cos(x1) - 6. x2 - 51.


                      x1 cos(x1) + 10. x2 + 85.


               29.9699774898013363718147183842 - 12. x4


              -18.0300225101986636281852816158 - 12. x4


              -19.5816890726838686776668041424 - 12. x4


              -42.0300225101986636281852816158 + 20. x4


              -43.5816890726838686776668041424 + 20. x4


               37.9699774898013363718147183842 + 20. x4


               36.4183109273161313223331958576 + 20. x4


               2.96997748980133637181471838419 - 21. x3


               1.41831092731613132233319585757 - 21. x3


               2.96997748980133637181471838419 - 5. x3


               1.41831092731613132233319585757 - 5. x3


               2.96997748980133637181471838419 + 11. x3


               1.41831092731613132233319585757 + 11. x3


               2.96997748980133637181471838419 + 27. x3


               1.41831092731613132233319585757 + 27. x3


               47.9699774898013363718147183842 - 6. x2


               46.4183109273161313223331958576 - 6. x2


              -72.0300225101986636281852816158 + 10. x2


              -73.5816890726838686776668041424 + 10. x2


               -48.0300225101986636281852816158 - 6. x2


               -49.5816890726838686776668041424 - 6. x2


               87.9699774898013363718147183842 + 10. x2


               86.4183109273161313223331958576 + 10. x2


                   62.4389036618089549324595962468


                   14.4389036618089549324595962468


                               "-----"


                 sol := {x1 = RootOf(tan(_Z) _Z - 1)}


                   -105.561096338191045067540403753


                   -25.5610963381910450675404037532


                   -33.5610963381910450675404037532


                   -81.5610963381910450675404037532


                   54.4389036618089549324595962468


                   134.438903661808954932459596247


                   65.9699774898013363718147183842


                   64.4183109273161313223331958576


                   17.9699774898013363718147183842


                   16.4183109273161313223331958576


                   -102.030022510198663628185281616


                   -103.581689072683868677666804142


                   -22.0300225101986636281852816158


                   -23.5816890726838686776668041424


                   -30.0300225101986636281852816158


                   -31.5816890726838686776668041424


                   -78.0300225101986636281852816158


                   -79.5816890726838686776668041424


                   57.9699774898013363718147183842


                   56.4183109273161313223331958576


                   137.969977489801336371814718384


                   136.418310927316131322333195858

> plot(1/(t*tan(t)-1),t=-3..5);

> 
