anonymous
  • anonymous
Consider the function f(x,y)=5x−9y+4xy−7(x^2)+6(y^2) defined in the unit square 0
Mathematics
jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
it appears to be hyperbolic ......
amistre64
  • amistre64
we can get a vector derivative if we take the gradient: but I aint sure how that would help yet
amistre64
  • amistre64
f(x,y)=5x−9y+4xy−7(x^2)+6(y^2) fx(x,y) = 5 +4y -14x fy(x,y) = -9 +4x +12y

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amistre64
  • amistre64
gf = (5 +4y -14x , -9 +4x +12y) can also define the normal to the surface; when this is pointing straight up or down would give you a tangent plane for a min or max right?
amistre64
  • amistre64
straight up is the same as (0,y); so id say make x=0 for starters ... just a hunch
amistre64
  • amistre64
gf = (5 +4y , -9 +12y)
anonymous
  • anonymous
nice multivariable
amistre64
  • amistre64
that mighta been a wrong step lol
amistre64
  • amistre64
aint it tho :)
amistre64
  • amistre64
gf = (5 +4y -14x , -9 +4x +12y) maybe when 5 +4y -14x = 0
anonymous
  • anonymous
I don't remember how to do this.. but we dealing with a gradient mic in one of my classes
anonymous
  • anonymous
mic check one two one two
amistre64
  • amistre64
5 +4y -14x = 0 y = 14x-5 x = 4y +5 ----- ------ 4 14
anonymous
  • anonymous
can you use LaTeX here?
amistre64
  • amistre64
you can \(\try\)
amistre64
  • amistre64
when: 5 +4y -14x = -9 +4x +12y we might get a zero derivative.... 5 + 4y -14x 9 -12y -4x ----------- 14 -8y -18x = 0 18x +8y = 14 ... i wonder...
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=5x%E2%88%929y%2B4xy%E2%88%927%28x^2%29%2B6%28y^2%29
amistre64
  • amistre64
i was sooo close lol add the gradient parts and do something....
amistre64
  • amistre64
i was on the right track; when the x and y parts of the gradient =0 we got a tangent plane that is flat.... to indicate a high and low
amistre64
  • amistre64
18x +8y = 14; we can use values between 0 and 1 to find out what works now
amistre64
  • amistre64
the line y=-(18x+14)/8 should give us the answers right? or y = -(9x+7)/4
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=18x+%2B8y+-+14%3D0

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