MediumCalculusca-363

Second Directional Derivative Value

Problem

For a twice differentiable function, the second derivative along a direction v is (v^T H v) / (v^T v), where H is the Hessian at the point.

Given the Hessian as nested rows and a nonzero direction vector, return the second directional derivative.

Hint

Form H v, then dot it with v and normalize by v dot v.

case 1

in: [[[1,0],[0,1]],[1,0]]

expected: 1

case 2

in: [[[2,1],[1,2]],[1,1]]

expected: 3

case 3

in: [[[0,1],[1,0]],[1,-1]]

expected: -1

Starter codePython

def second_directional_derivative(h, v):
    # Your code here
    pass

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