Multivariable calculus - Second partial derivative test intuition

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/optimizing-multivariable-functions-videos/v/second-partial-derivative-test-intuition The second partial derivative test is based on a formula which seems to come out of nowhere. Here, you can see a little more intuition for why it looks the way it does.