For function
Find all stationary points and describe their nature.
So this is what I did, first I took the two partial derivatives.
Allow the partial derivatives to equal zero to equate the critical points.
For I divided both sides by y (not sure if this was a mistake or not), and for I divided both sides by x.
This left me with:
and
From here, do I allow the two equations to equal each other and equate from there, or is that just going to get me into a muddle?
I can't seem to work out a simple method to finding values that satisfy both equations aside from guessing (embarrasing I know).
Thanks in advance,
Thanks to both of you for helping. I've got two of the solutions so far, but I'm told that there are four solutions. From equations (1) and (2) I can see that I can't get another solution because they're both linear.
This makes me think that the other two solutions [besides (0,0) and (2/3,4/3)] have one zero in them, ie: (0,y) and (x,0). In which case I would have to take the first piece of advice given and re-arrange my two formulae and sub them in.
However my algebra skills are lacking today and I can't seem to seperate x or y in either of the formulae without dividing by y or x respectively.
A pointer for the first step or two would be appreciated.
PS, I think my mind's just in a bit of a fluster because I've been studying too many consecutive hours for my exam tomorrow. Sorry if I'm missing something really obvious.
Thanks,