(%i1) 2* sin(%pi / 6 * x);
				       %pi x
(%o1) 				 2 sin(-----)
					 6

(%i2) "Funktionsuntersuchung"$


(%i3) f(x) := 2* sin(%pi / 6 * x);
					   %pi
(%o3) 			     f(x) := 2 sin(--- x)
					    6

(%i4) "Schnittpunkt mit y-Achse"$


(%i5) f(0);
(%o5) 				       0

(%i6) "Nullstellen"$


(%i7) solve(2* sin(%pi / 6 * x)= 0, x);

`solve' is using arc-trig functions to get a solution.
Some solutions will be lost.
(%o7) 				    [x = 0]

(%i8) ev(%,numer);
(%o8) 				    [x = 0]

(%i9) "1. Ableitung"$


(%i10) diff(f(x),x) ;
					%pi x
				%pi cos(-----)
					  6
(%o10) 			        --------------
				      3

(%i11) sqfr(%);
					%pi x
				%pi cos(-----)
					  6
(%o11) 			        --------------
				      3

(%i12) "Extremstellen"$


(%i13) solve( %th(2) = 0,x);

`solve' is using arc-trig functions to get a solution.
Some solutions will be lost.
(%o13) 				    [x = 3]

(%i14) ev(%,numer);
(%o14) 				    [x = 3]

(%i15) "2. Ableitung"$


(%i16) diff(f(x),x,2) ;
				    2	  %pi x
				 %pi  sin(-----)
					    6
(%o16) 			       - ---------------
				       18

(%i17) sqfr(%);
				    2	  %pi x
				 %pi  sin(-----)
					    6
(%o17) 			       - ---------------
				       18

(%i18) "Wendestellen"$


(%i19) solve( %th(2) = 0,x);

`solve' is using arc-trig functions to get a solution.
Some solutions will be lost.
(%o19) 				    [x = 0]

(%i20) ev(%,numer);
(%o20) 				    [x = 0]

(%i21) "3. Ableitung"$


(%i22) diff(f(x),x,3) ;
				    3	  %pi x
				 %pi  cos(-----)
					    6
(%o22) 			       - ---------------
				       108

(%i23) sqfr(%);
				    3	  %pi x
				 %pi  cos(-----)
					    6
(%o23) 			       - ---------------
				       108

(%i24) "Stammfunktion"$


(%i25) integrate(f(x), x);
					 %pi x
				  12 cos(-----)
					   6
(%o25) 			        - -------------
				       %pi

(%i26) sqfr(%);
					 %pi x
				  12 cos(-----)
					   6
(%o26) 			        - -------------
				       %pi

(%i27) functions;
(%o27) 				    [f(x)]

(%i28) plot2d([f(x)],[x,0,12],[y,-10,10],[gnuplot_preamble,"set grid; set zeroaxis linetype -1;"]);
(%o28) 

(%i29)