Basic Examples (7)
Basic Examples
(7)
Find the stationary points of a function of one variable:
In[17]:=
statPoints=[t^2Exp[-t^2],{t}]
Out[17]=
Minima{{0,{t0}}},Maxima,{t-1},,{t1}
1
1
Plot the function and its stationary points found above:
In[22]:=
Plot[t^2Exp[-t^2],{t,-5,5},EpilogJoin[{Red,PointSize@Large},Point[{#〚2,1,2〛,#〚1〛}]&/@Flatten[Values[statPoints],1]]]
Out[22]=
———
Findthestationarypoints
In[19]:=
Out[19]=
Minima-1,x,-1,x,Maxima1,x
In[20]:=
Out[20]=
Inflection0,x,0,x
———
Findthestationarypoints
In[22]:=
Out[22]=
Minima-1,x-,Maxima1,x
π
2
π
2
In[23]:=
Out[23]=
Inflection{{0,{x0}},{0,{x-3π}},{0,{x-2π}},{0,{x-π}},{0,{xπ}},{0,{x2π}},{0,{x3π}}}
———
Find stationary points of a function of two variables:
In[25]:=
Out[25]=
Saddle-,x-,y-,,x-,y,{0,{x0,y0}}
16
75
15
2
5
2
15
16
75
15
2
5
2
15
———
Find stationary points of a function of three variables when restricting to a plane:
In[26]:=
Out[26]=
Saddle{{0,{x0,y0,z100}},{0,{x0,y100,z0}},{0,{x100,y0,z0}}}
———
Using the "Type" option will return only stationary points of the given type:
In[34]:=
Out[34]=
{{2,{x0,y0}}}
In[35]:=
Out[35]=
,x-,y-,,x-,y,,x,y-,,x,y
229
2
15
2
15
2
229
2
15
2
15
2
229
2
15
2
15
2
229
2
15
2
15
2
In[23]:=
Out[23]=
{{-1.32116,{x0.673612,y-0.739085}}}
———
Using as the second argument gives an of all stationary points:
In[39]:=
Out[39]=
Minima{{2,{x0,y0}}},Maxima,x-,y-,,x-,y,,x,y-,,x,y,Saddle,x0,y-,,x0,y,,x-,y0,,x,y0
229
2
15
2
15
2
229
2
15
2
15
2
229
2
15
2
15
2
229
2
15
2
15
2
233
4
15
2
233
4
15
2
233
4
15
2
233
4
15
2
Properties and Relations (2)
Properties and Relations
(2)
Possible Issues (2)
Possible Issues
(2)