anonymous
  • anonymous
The function g(x,y) = x^4+y^3 has a critical point at (0,0). What sort of critical point is it?
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
its either a min, a max, or a saddle that is a min of one and a max of the other id assume
amistre64
  • amistre64
gx = 4x^3 gxx = 12x^2 gxy = 0 gy = 3y^2 gyy = 3y gyx = 0
amistre64
  • amistre64
|dw:1332513423980:dw|

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More answers

anonymous
  • anonymous
The second derivative test fails but i there is another method the has something to do with completing the square
amistre64
  • amistre64
if we graph the projections into the zx and zy planes we can see that its a min
amistre64
  • amistre64
err, something close to a min :)
amistre64
  • amistre64
|dw:1332513509119:dw|
amistre64
  • amistre64
im not really sure WHAT to call it :) but there is some formula that I can never recall fxx+fyy-fxy or some such
anonymous
  • anonymous
like i dont think i am suppossed to be graphing this. There shld be some method.
Zarkon
  • Zarkon
is this your first course in multivariable calculus?
anonymous
  • anonymous
yes
Zarkon
  • Zarkon
then just look at the graph.
Zarkon
  • Zarkon
and it is a saddle point
amistre64
  • amistre64
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anonymous
  • anonymous
ok thanks
amistre64
  • amistre64
i was thinking of calling it a chair point :)
Zarkon
  • Zarkon
that would work too ;)
anonymous
  • anonymous
hahah thanks guys :)
anonymous
  • anonymous
sorry for driving u crazy zarkon
Zarkon
  • Zarkon
that is fine I'll live. :)

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