Second Derivative Test - Two Variables (KristaKingMath)

Second Derivative Test calculus problem example.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[joeface]

I just wanted to say thank you so much my teacher didn't really explain this well, so you are a life saver!!!

[asemnafiz]

Perfect explanation! So clear! Thank a lot for the help! You have been helping me since Calc1 and now I'm in Calc3.

[mohamedeldaly]

Where does that equation D(x, y) come from and why do the rules you said at the end apply?

[akillarazarar]

I rage-quit my continuous optimization class, opened the laptop and watched this video. 10+min later I came back to class and I was the only one who could follow... Some people know how to expalin things and some people don't (you know, and my professor most certainly doesn't). Thank you very much for sharing the knowledge :) It helped a lot.

[ridwan]

oh my heavens I love you! I dont know why my 80 year old Calc 3 professor couldnt explain it like this!

[goyo]

you've helped me so much throughout my undergrad career, thank you!!

[alexanderkuku]

It's lovely and you are very lucid all through. Nice video. Love you.

[fausttino]

Wow! you made it appear so easy. This will be the 2nd time I am repeating calc 3 and you have just helped me get ready for the exam that will finally get me past this to the next level keep up the good work, Wish I wasn't such a broke college student lol I will subscribe to your website and pay the monthly fee

[peque]

Thank you very much! Your videos are so helpful.

[dpyp]

very awesome video, thank you so much for your efforts.
u can do one thing.. put 2 as r, 2 as s and last term as t. and find rt-s*2. it would be easily remember ed

[kristakingmath]

The process is explained here: integralcalc . com/how-I-create-my-videos/ and the chalkboard is just an image :)

[starbonjr]

Do you only need to look at the second dervative with respect x and D(x, y) and not the Fyy in determining the relative extrema?

[KLearningCoach]

Thank you so much! This was very helpful!!!

[pothulabhargav]

what if  D(x, y) >0 and second derivative w.r.t   x  was 0...???

[secondbelarus]

Non multa, sed multum.
All clearly put, thank you.

[sstruyf]

great explanation. i was getting confused!

[artie]

how would I go about a question formatted similarly, 2 variables, but the answer expected is (x, y, z) values ? where did the Z come from

[thatomothoagae]

Hi ma’am. Which multivariable calculus book do you recommend?

[stockbroker]

Please I need to know what is it about Relative Extrema and Inflection points doing them with derivatives.

[peacebewu]

when do we use this and when do we use implicit differentiation?