Hi, I have to find the co-ordinates where the line y=-x+1 intersects f(x,y) = x^2 + y^2 -xy - y -1
I can do this with explicit functions by making them equal, but it doesn't work with this.
The actual question asks for the co-ordinates where the tangent to f(x,y), is at 45 deg to the horizontal. So I found the gradient function which = 1 (that got me the linear equation), now i'm stuck.
Not sure if this should be in calc. section, so sorry if I got it wrong.
Oh ok, i was going about it the wrong way thanks.
As an aside:- I managed to get those co-ordinates for x earlier in the question, where it asked for the stationary points. Is it just the nature of the shape that the x co-ordinates are the same, when the gradient is 0 and 45 deg?
Also, when working out the S.P I got four possible Y values, and only knew which ones to use by plotting the graph, is there another mathematical way of doing it?