Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Critical Points & Max/Min?
f(x, y) = 2x^3 - 6x^2 + y^3 + 3y^2 - 48x - 45y
a) Find the critical points where the function is optimized
b) Max or Min
1 Answer
- Linda KLv 51 decade agoFavorite Answer
fx(x,y) = 6x^2 - 12x -48
setting = 0 and solving, x = 3 or -1
fy(x,y) = 3y^2 + 6y - 45
setting = 0 and solving, y = -5 or 3
I believe you make all possible combinations:
(3, -5), (3, 3), (-1, -5), (-1, 3)
fxx(x,y) = 12x - 12 = 12(x - 1)
fyy(x,y) = 6y + 6= 6(y + 1)
fxy(x,y) = fyx(x,y) = 0
Thus,
d = fxx(x,y)fyy(x,y)- [fxy(x,y)]^2
d = 72(x - 1) (y + 1) - 0
for (3, -5) d <0 max
for (3, 3) d >0 min
for (-1, -5) d >0 min
for (-1, 3) d < 0 max
Hope it's right--little rusty
