Second Partial Derivative Test, Conceptually | Multivariable Calculus

This calculus 3 video will go into the second partial derivative test for finding minimums, maximums, or saddle points of a multivariable function of two or more input variables. Mostly conceptual explanation.

[Alex-ummx]

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[broysthgaming]

I have been playing around with second derivative test for a week now. But steel could not figure out why to squaring and subtracting the last term?

[oceangangocean]

FAQ from my homie:
- Wait, is the test just to find if there's a saddle?
You're evaluating D at a critical point.
To sum up, if D > 0, there's either a min or max
If D < 0 there's a saddle
If D = 0, we have no clue
So the test itself and the sign of D determines whether there's a saddle, min max, or inconclusive
But then upon further inspection of the sign of partial f/partial x and partial f/partial y, in the case that they agree, if they're positive (concave up), you'll get min, if they're negative (concave down), you'll get max
- How do you find min or max point?
A critical point would need both partial f/partial x and partial f/partial y equal to zero. So after solving that system of equations, we can get a critical point.
- Is partial derivative derivative in a single direction?
Yes, partial f/partial x looks at the change in the x direction
partial f/ partial y looks at the change in the y direction
- Is f(x, y) = z?
In this case yeah, I think I use z as the function in this video.

Reply with more questions!!