Question

to find the range of f(x,y), would we find that partials fx and fy equal to 0 ?

Answer 1

I think that would give you the locations where the rate of change is 0 with respect to each variable rather than the range.

Answer 2

right, it could be a saddleback; a min or a max ....

Answer 3

fxx and fyy would determine cave i think

Answer 4

Ah, maybe I'm misunderstanding range. What does it mean in this context?

Answer 5

it would provide a point of interest; the actual value would depend on plugging x and y back into f(x,y)

Answer 6

all possible outputs ...

Answer 7

That would be a way to find those points of interest, so it would give you the range of the function if you had a "nice" function.

Answer 8

spose

f(x,y) = ln(4-x^2-9y^2) determine domain and range

Answer 9

nice functions dont exist lol

Answer 10

Lol, I meant differentiable.

Answer 11

fx = -2x/(4-x^2-9y^2)

fy = -18y/(4-x^2-9y^2)

at x=0 and y=0 we have a max since this things an eggy ellipse

range is up to ln(4)

Answer 12

but is the lower limit -inf? or 0?

Answer 13

That makes sense to me, but I'm not sure how to find out that lower limit.

Answer 14

http://www.wolframalpha.com/input/?i=range+f%28x%2Cy%29%3Dln%284-x%5E2-9y%5E2%29

the wolf says unable to determine range lol

Answer 15

Yeah, I looked at that, too, lol.

Answer 16

Looking at it intuitively, 4-x^2-9y^2 can get arbitrarily close to 0, which should mean that ln(4-x^2-9y^2) should be able to approach negative infinity.

Answer 17

which is what I was thinking as well; which is why there isnt another fx or fy to zero out of

Answer 18

http://web.monroecc.edu/manila/webfiles/calcNSF/JavaCode/CalcPlot3D.htm

thats useful

Answer 19

This is sexy.

Answer 20

lol