We will use these 21 angles to create a circle of points around (a,b)
7
Expression 8: "t" equals left bracket, 0 , StartFraction, pi Over 10 , EndFraction , StartFraction, 2 pi Over 10 , EndFraction , ... , 2 pi , right brackett=0,π10,2π10,...,2π
equals=
00
0.3 1 4 1 5 9 2 6 5 3 5 90.314159265359
0.6 2 8 3 1 8 5 3 0 7 1 80.628318530718
0.9 4 2 4 7 7 7 9 6 0 7 70.942477796077
1.2 5 6 6 3 7 0 6 1 4 41.25663706144
1.5 7 0 7 9 6 3 2 6 7 91.57079632679
1.8 8 4 9 5 5 5 9 2 1 51.88495559215
2.1 9 9 1 1 4 8 5 7 5 12.19911485751
2.5 1 3 2 7 4 1 2 2 8 72.51327412287
2.8 2 7 4 3 3 3 8 8 2 32.82743338823
3.1 4 1 5 9 2 6 5 3 5 93.14159265359
3.4 5 5 7 5 1 9 1 8 9 53.45575191895
3.7 6 9 9 1 1 1 8 4 3 13.76991118431
4.0 8 4 0 7 0 4 4 9 6 74.08407044967
4.3 9 8 2 2 9 7 1 5 0 34.39822971503
21 element list
8
The circle of points will have radius r
9
Expression 10: "r" equals 0.1r=0.1
negative 10−10
1010
10
This table evaluates f(a,b) - f(c,d) where the (c,d) points are on the circle of radius r centered at point (a,b). If the values in the second column are ALL POSITIVE then (a,b) is a local maximum. If the values in the second column are all ALL NEGATIVE then (a,b) is a local minimum. If the values in the second column are a MIX OF POSITIVE AND NEGATIVE then (a,b) is a saddle point.
11
"t"t
"f" left parenthesis, "a" , "b" , right parenthesis negative "f" left parenthesis, "a" plus "r" sin left parenthesis, "t" , right parenthesis , "b" plus "r" cos left parenthesis, "t" , right parenthesis , right parenthesisfa,b−fa+rsint,b+rcost