Question

Locate the critical point of the function.
f(x,y)=2 − x^(2) − 8x − y^(2)+6y

Need all the help i can get i have an exam in 4 hours

Answer 1

find 4 things:

Fx, Fy, Fxx, Fyy, Fxy .... ok, 5 things but only the doubles are needed

Answer 2

i think i got down to the critical points, i found x to be -4 and y to be 3…
then do i plug those in?

Answer 3

D = Fxx Fyy - (Fxy)^2

if D > 0 and Fxx >0, then (a,b) is a relative min
if D > 0 and Fxx <0, then (a,b) is a relative max

if D < 0, its a saddle point
if D = 0, then it may or maynot be sufficient

Answer 4

let me check ..

f(x,y)=2 − x^(2) − 8x − y^(2)+6y

Fx = -2x-8
Fxx = -2
Fxy = 0

Fy = -2y+6
Fyy = -2

D = 4

D > 0, Fxx < 0 so there is a max located someplace

Answer 5

x=4, y=3 seems to fit the bill

Answer 6

hmm, max = -4,3 yes

Answer 7

lol, i was thinking -2x+8 .... silly me

Answer 8

haha its okay, so is that the only two critical points?

Answer 9

that is 1 critical point, and we found it since this is an upside down parabolic cone

Answer 10

how did you find out it was an upside down parabolic cone? cause i need to know how to graph on my exam