Question

Consider the function f(x,y)=5x−9y+4xy−7(x^2)+6(y^2) defined in the unit square 0
14 years ago

Answer 1

it appears to be hyperbolic ......

Answer 2

we can get a vector derivative if we take the gradient: but I aint sure how that would help yet

Answer 3

f(x,y)=5x−9y+4xy−7(x^2)+6(y^2)

fx(x,y) = 5 +4y -14x

fy(x,y) = -9 +4x +12y

Answer 4

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?

Answer 5

straight up is the same as (0,y); so id say make x=0 for starters ... just a hunch

Answer 6

gf = (5 +4y , -9 +12y)

Answer 7

nice multivariable

Answer 8

that mighta been a wrong step lol

Answer 9

aint it tho :)

Answer 10

gf = (5 +4y -14x , -9 +4x +12y)

maybe when 5 +4y -14x = 0

Answer 11

I don't remember how to do this.. but we dealing with a gradient mic in one of my classes

Answer 12

mic check one two one two

Answer 13

5 +4y -14x = 0

y = 14x-5 x = 4y +5
----- ------
4 14

Answer 14

can you use LaTeX here?

Answer 15

you can \(\try\)

Answer 16

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...

Answer 17

http://www.wolframalpha.com/input/?i=5x%E2%88%929y%2B4xy%E2%88%927%28x^2%29%2B6%28y^2%29

Answer 18

i was sooo close lol

add the gradient parts and do something....

Answer 19

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

Answer 20

18x +8y = 14; we can use values between 0 and 1 to find out what works now

Answer 21

the line y=-(18x+14)/8 should give us the answers right?

or

y = -(9x+7)/4

Answer 22

http://www.wolframalpha.com/input/?i=18x+%2B8y+-+14%3D0