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# Partial differentiation help!!! watch

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1. Hi

Stuck on this one question, would really appreciate some help.

Show that the minimum value of:

is

where c is a constant

Calling the above equation z i tried partially differentiating it in terms of x and y, and then equalling both equations to zero. Tried different combinations of canceling out and re-arranging but cant seem to get rid of the the x's and y's.

Would appreciate any help,

Thanks
2. Post your working. It should only be a few lines.

What does that exactly mean? And how do you recognise it?

Thanks
4. The given function is symmetric in x and y, ie the function does not change if x and y are interchanged.
5. Thank Youu
6. Since we're on the topic,

Is x = y assumption valid?
7. yeh i got the same thing, i just made a simple mistake when dividing. Its quite an easy question infact.

8. Well, obviously it's true here. But there are lots of symmetric minimization problems with asymmetric solutions - for example

Minimize xyz-(x+y+z) given that x^2+y^2+z^2 = 2

has its minimum at x=y=1, z= 0 (plus 5 other obviously related solutions).

So no, I don't see it's valid without justification.
9. (Original post by DFranklin)
Well, obviously it's true here. But there are lots of symmetric minimization problems with asymmetric solutions - for example

Minimize xyz-(x+y+z) given that x^2+y^2+z^2 = 2

has its minimum at x=y=1, z= 0 (plus 5 other obviously related solutions).

So no, I don't see it's valid without justification.
So how then do you justify x = y in the the original problem?
10. The approach deepdawg originally suggested seems to work fine, as far as I can see.
11. (Original post by DFranklin)
The approach deepdawg originally suggested seems to work fine, as far as I can see.
Yes it did. Partial differentiation.

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