pringle points

Question 1

how to find stationary points of a multi variable function

Answer 1

points where df/dx = df/dy = df/dz = … = 0

Question 2

how to classify a 2D stationary point

Answer 2

saddle point:
- hessian determinant < 0
minimum:
- hessian > 0
- f_xx > 0
maximum:
- hessian > 0
- f_xx < 0

Question 3

what is the hessian matrix

Answer 3

• matrix of a function’s second order partial derivatives
• down the diagonal: xx, then yy, zz, etc
• determinant used to classify stationary points

Question 4

how to classify a stationary point of any dimension

Answer 4

minimum:
- hessians of all dimensions (including 1) positive
- so starts with f_xx > 0
maximum:
- hessians of each dimension alternate in sign
- starts with f_xx < 0