(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

These are two problems from my assignment that are due tomorrow! Plz, help as you can.

1)Show that f(x,y) = (y - x)(y - 3x^2) attains a local minimum on every straight line through the origin and that this occurs at (0,0). Does f have a local minimum at (0,0)?

2)Assuming that f_x and f_y both exist at (x,y), prove that if

[itex]\lim_{(h,k)\rightarrow(0,0)}\dfrac{f(x+h, y) - f(x,y) - f_{x}(x,y)h - f_{y}(x,y)k}{\sqrt{h^2 + k^2}}[/itex]

exists, the limit is 0.

2. Relevant equations

3. The attempt at a solution

For the first one I tried Lagrange's multipliers but became a mess with all the algebra, leaving me with the impression that this might be done more easily using something that I might have missed in class.

For the 2nd one, honestly, no clue. I left my assignment for the last day, because I had so many other stuff to do. Now I'm really in trouble. Thanks for all your help.

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# Homework Help: Constrained extrema

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