Basic Examples (4)
Basic Examples
(4)
Find the inflection points of a cubic function:
In[33]:=
func=x^3;inflPts=[func,x]
Out[34]=
{{x0}}
Plot the function and its inflection points found above:
In[35]:=
Plot[{func},{x,-3,3},EpilogJoin[{Red,PointSize@Large},Point[{#〚1,2〛,func/.#}]&/@inflPts]]
Out[35]=
Repeat the calculation, classifying inflection points:
In[36]:=
Out[36]=
{{x0,Properties{Stationary,Rising}}}
———
Find and classify the inflection points of a polynomial function:
In[55]:=
func=1+3+;inflPts=[func,x,"Properties"]
2
x
3
x
Out[56]=
{{x-1,Properties{Non-stationary,Falling}}}
Plot the function and its inflection points:
In[57]:=
Plot[{func},{x,-4,2},EpilogJoin[{Red,PointSize@Large},Point[{#〚2〛,func/.#}]&/@inflPts〚All,1〛]]
Out[57]=
———
Find and classify the inflection points of another polynomial function:
In[37]:=
func=(x-1)(x-2)(x-3)(x-3.2);inflPts=[func,x,"Properties"]
Out[38]=
{{x1.79338,Properties{Non-stationary,Rising}},{x2.80662,Properties{Non-stationary,Falling}}}
Plot the function and its inflection points:
In[39]:=
Plot[{func},{x,0.7,3.9},EpilogJoin[{Red,PointSize@Large},Point[{#〚2〛,func/.#}]&/@inflPts〚All,1〛]]
Out[39]=
———
Find and classify the inflection points of a trigonometric function:
In[42]:=
func=Sin[x];inflPts=[func,x,"Properties"]
Out[43]=
x,Properties{Non-stationary,Rising},x,Properties{Non-stationary,Falling}
Plot the function and a single cycle's worth of its inflection points:
In[44]:=
Plot[{func},{x,-5,7},EpilogJoin[{Red,PointSize@Large},Point[{#〚2〛,func/.#}]/.0&/@inflPts〚All,1〛]]
1
Out[44]=
Options (2)
Options
(2)
Properties and Relations (3)
Properties and Relations
(3)