MediumCalculusca-071

Saddle Point Check

Problem

Classify the critical point of a quadratic whose Hessian is H = [[p, q], [q, r]] at that point.

Let det = p*r - q^2. Return "saddle" if det < 0, "minimum" if det > 0 and p > 0, "maximum" if det > 0 and p < 0, and "degenerate" if det == 0.

Hint

The second derivative test uses the determinant and the sign of H_xx.

case 1

in: [2,0,2]

expected: "minimum"

case 2

in: [-2,0,-2]

expected: "maximum"

case 3

in: [1,2,1]

expected: "saddle"

case 4

in: [0,0,0]

expected: "degenerate"

case 5

in: [3,1,1]

expected: "minimum"

Starter codePython

def saddle_check(p, q, r):
    # Return "minimum", "maximum", "saddle", or "degenerate"
    # Your code here
    pass

5 test cases · run your code against them in the editor