Classify 2D Critical Point

We will use these 21 angles to create a circle of points around (a,b)

Uttryck 8: "t" equals left bracket, 0 , StartFraction, pi Over 10 , EndFraction , StartFraction, 2 pi Over 10 , EndFraction , ... , 2 pi , right bracket

equals

0.3 1 4 1 5 9 2 6 5 3 5 9

0.6 2 8 3 1 8 5 3 0 7 1 8

0.9 4 2 4 7 7 7 9 6 0 7 7

1.2 5 6 6 3 7 0 6 1 4 4

1.5 7 0 7 9 6 3 2 6 7 9

1.8 8 4 9 5 5 5 9 2 1 5

2.1 9 9 1 1 4 8 5 7 5 1

2.5 1 3 2 7 4 1 2 2 8 7

2.8 2 7 4 3 3 3 8 8 2 3

3.1 4 1 5 9 2 6 5 3 5 9

3.4 5 5 7 5 1 9 1 8 9 5

3.7 6 9 9 1 1 1 8 4 3 1

4.0 8 4 0 7 0 4 4 9 6 7

4.3 9 8 2 2 9 7 1 5 0 3

Lista med 21 element

The circle of points will have radius r

Uttryck 10: "r" equals 0.1

negative 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.

"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 parenthesis
r1c1: 0	r1c2: negative 0.1 1 2 2	r1c3:
r2c1: 0.3 1 4 1 5 9 2 7	r2c2: negative 0.1 1 4 5 3 3 3 6	r2c3:
r3c1: 0.6 2 8 3 1 8 5 3	r3c2: negative 0.0 9 6 8 6 6 6 7 3	r3c3:
r4c1: 0.9 4 2 4 7 7 8	r4c2: negative 0.0 6 5 4 2 4 4 7	r4c3:
r5c1: 1.2 5 6 6 3 7 1	r5c2: negative 0.0 3 2 0 2 5 5 2 6	r5c3:
r6c1: 1.5 7 0 7 9 6 3	r6c2: negative 0.0 1	r6c3:
r7c1: 1.8 8 4 9 5 5 6	r7c2: negative 0.0 0 8 9 8 6 2 5 2	r7c3:
r8c1: 2.1 9 9 1 1 4 9	r8c2: negative 0.0 3 0 6 3 1 4 0 6	r8c3:
r9c1: 2.5 1 3 2 7 4 1	r9c2: negative 0.0 6 7 2 9 6 5 4 9	r9c3:
r10c1: 2.8 2 7 4 3 3 4	r10c2: negative 0.1 0 4 7 8 5 7 7	r10c3:
r11c1: 3.1 4 1 5 9 2 7	r11c2: negative 0.1 2 8 2	r11c3:
r12c1: 3.4 5 5 7 5 1 9	r12c2: negative 0.1 2 8 2 9 7 1 8	r12c3:
r13c1: 3.7 6 9 9 1 1 2	r13c2: negative 0.1 0 5 3 3 8 8 1	r13c3:
r14c1: 4.0 8 4 0 7 0 4	r14c2: negative 0.0 6 8 6 7 3 6 6 7	r14c3:
r15c1: 4.3 9 8 2 2 9 7	r15c2: negative 0.0 3 2 4 9 7 6 6 2	r15c3:
r16c1: 4.7 1 2 3 8 9	r16c2: negative 0.0 1	r16c3:
r17c1: 5.0 2 6 5 4 8 2	r17c2: negative 0.0 0 8 5 1 4 1 1 6	r17c3:
r18c1: 5.3 4 0 7 0 7 5	r18c2: negative 0.0 2 7 3 8 2 2 0 9	r18c3:
r19c1: 5.6 5 4 8 6 6 8	r19c2: negative 0.0 5 8 8 2 4 4 1 3	r19c3:
r20c1: 5.9 6 9 0 2 6	r20c2: negative 0.0 9 1 0 2 1 9 4 7	r20c3:
r21c1: 6.2 8 3 1 8 5 3	r21c2: negative 0.1 1 2 2	r21c3:

Uttryck 13:

driven av