Gradients, Hessians, and All Those Derivative Tests

This video derives the gradient and the hessian from basic ideas. It shows how the gradient lets you find the directional derivative, and how the hessian lets you compute the directional second derivative. Finally, I talk about the first and second derivative tests in higher dimensions, which lets you determine whether a point is a local maximum or a minimum.

Chapters:
Intro - 0:00
Gradients and Directional Derivatives - 2:14
Hessians and Directional Second Derivatives - 9:14
Derivatives Tests - 12:09

[juniorcyans]

Thank you very much! I’m taking linear algebra after having used it for my physics classes a lot, and my professor didn’t have enough time to explain what Hessian means. This morning your video popped up and things are connected in a sudden!