Local extreme

[know]

How to find local extreme:
g(x,y)=√(9-x^2-y^2)

I tried to work, but I don't understand very well...
If we find gx=-x/√(9-x^2-y^2), than x=0
gy=-y/(9-x^2-y^2), than y=0
S(0,0)
-Is that correct?

How to find gxx, gxy, gyx, gyy?

 

[Deleted member 4993]

How to find local extreme:
g(x,y)=√(9-x^2-y^2)

I tried to work, but I don't understand very well...
If we find gx=-x/√(9-x^2-y^2), than x=0
gy=-y/(9-x^2-y^2), than y=0
S(0,0)
-Is that correct?

How to find gxx, gxy, gyx, gyy?

You write:

If we find g_x=-x/√(9-x^2-y^2), than x=0​

​

Your expression for gx gy are correct - but I do not understand the part "than x=0".

Please read: https://tutorial.math.lamar.edu/classes/calciii/relativeextrema.aspx​

To find g_xx, differentiate g_x with respect to x

To find g_xy, differentiate g_y with respect to y

To find g_yy, differentiate g_y with respect to y

Make sure that you got g_xy and g_yx are equal.

 

[know]

I have to find critical point, and answer is that Minimum or Maximum
(0,0)

 

[Deleted member 4993]

I have to find critical point, and answer is that Minimum or Maximum(0,0)

Please read: https://tutorial.math.lamar.edu/classes/calciii/relativeextrema.aspx

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this problem.

 

[JeffM]

I doubt “know” is a single person. In May, that pseudonym could not do a simple algebra problem dealing with percentages.

% question

Worker BB received a salary in the amount of € 1100 in the previous month, which is 20% less than the salary in the current month. What is the salary in the current month? a) 1400 b) 1356 c) 1320 d) 1375 If we subtract 20% from 1320, we get 1056. The salary in the previous month was 1100...

www.freemathhelp.com

Now that same pseudonym is asking a question about multivariate calculus. It is impossible to explain multivariate calculus to someone who does not know algebra.

 

[Steven G]

I once had to tutor a student in calculus 3 who would have failed a basic arithmetic course. I was very disappointed in the math faculty for passing this student time after time. Would you believe that he was a math major. The department finally realized that he would not have a 3.0 average in his major (and can't graduate) so they convinced him to change his major. He changed to engineering! I suspect that you know how he did with that.

The point is that I believe that *know* might be in calculus 3.