ID any extrema of the function by recognizing its given form or its forms after completing the square. Verify your results by using the partial derivatives to locate any critical points and test for relative extrema.

g(x,y)=(25-(x-2)^2-y^2)^1/2

Question

ID any extrema of the function by recognizing its given form or its forms after completing the square. Verify your results by using the partial derivatives to locate any critical points and test for relative extrema. 

g(x,y)=(25-(x-2)^2-y^2)^1/2

anonymous · Answer

I just need to know what you guys got for critical points (I'm going to repost the equation...)

anonymous · Answer

$$\sqrt{25-(x-2)^2-y^2}$$

anonymous · Answer

For y I got 0 and for x I got $$2\sqrt{21}/21$$

anonymous · Answer

these are my derivatives: 

$$f _{x}=2-x/\sqrt{-x^2+4x-y^2+21}$$

and 

$$f_{y}=-y/\sqrt{-x^2+4x-y^2+21}$$

anonymous · Answer

$$\frac{\delta g(x,y)}{\delta x} = \frac{2-x}{ \sqrt{25 - (x-2)^2 - y^2}}$$

anonymous · Answer

yeah they look right

experimentx · Answer

Oo .. i thought i was at bottom :P

experimentx · Answer

* it was at

experimentx · Answer

seems all right ... http://www.wolframalpha.com/input/?i=extremum+%2825-%28x-2%29%5E2-y%5E2%29%5E1%2F2

anonymous · Answer

@experimentX    are you studying at MIT ?

anonymous · Answer

^ did you mean my deritatives or ciritcal points?

anonymous · Answer

sorry i was being  nosy on your profile

experimentx · Answer

lol ... you make me laugh. i'm just a poor loser at some stupid college.

anonymous · Answer

cant be such a stupid college, you seem really good at maths :D

anonymous · Answer

its not really about the college tbh, its the person. sorry, im from the uk and am unfamiliar with how it works, does college = university ? over here we have school, college, uni but america/uk words for things are different

experimentx · Answer

I'm from asia ... your name sounds rather like german

anonymous · Answer

haha see what i mean im useless at identifying anything..

yeah "eigenschmeigen" was the name of a recent piece of work our maths teacher set us on eigenvectors .. i think eigen is a german word

experimentx · Answer

identifying ... comes from experience. ingenuity is different matter .. BYW your cos proof was ingenious.

anonymous · Answer

aw thanks. im still stuck on the sine, i liked your solution of 4 , that one looked scary

experimentx · Answer

yeah .. i had to program it first ... later @ffm said that it has simple solution ... then i came up with it ... still there should be elegant proof ... you can't write that in your exam paper.
But i've to admit .. these guys are on whole different level than me.

experimentx · Answer

@eigenschmeigen and by the way ... what matters most in the long run is "drive" ... best of luck with your sine problem.

experimentx · Answer

*keep up with your sine problem

anonymous · Answer

so the critical points are 2,0 and not what I had above?