Find a critical point [.xo. yol of the function f(x, y) = -2 + x² - 64 y + 6 xy + y². [xo. Yol = What is the nature of the critical point? O a local maximum O inconclusive a saddle point O a local minimum

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Multivariable Calculus please help with these two questions, thank you!
Find a critical point [xo. yol of the function f(x, y) = -2 + x²-64y+ 6 xy + y².
[xo. yol =
What is the nature of the critical point?
O a local maximum
O inconclusive
O a saddle point
O a local minimum
Suppose we have the following information about the functions f(x, y), g(x, y), h(x, y) and k(x, y) at (0, 0). Complete the following table:
Function
f(x, y)
g(x, y)
h(x, y)
k(x, y)
d
ox
-(0, 0)
0
0
0
0
d
dy
2²
-(0,0) (0, 0)
dx2
0
0
0
0
T
-2
-2
1
dy2
(0,0)
-2
-1
-1
3
2²
dxdy
(0,0)
2
-1
Ċ
1
3
(0, 0) is
(No answer given)
(No answer given)
(No answer given)
(No answer given)
Transcribed Image Text:Multivariable Calculus please help with these two questions, thank you! Find a critical point [xo. yol of the function f(x, y) = -2 + x²-64y+ 6 xy + y². [xo. yol = What is the nature of the critical point? O a local maximum O inconclusive O a saddle point O a local minimum Suppose we have the following information about the functions f(x, y), g(x, y), h(x, y) and k(x, y) at (0, 0). Complete the following table: Function f(x, y) g(x, y) h(x, y) k(x, y) d ox -(0, 0) 0 0 0 0 d dy 2² -(0,0) (0, 0) dx2 0 0 0 0 T -2 -2 1 dy2 (0,0) -2 -1 -1 3 2² dxdy (0,0) 2 -1 Ċ 1 3 (0, 0) is (No answer given) (No answer given) (No answer given) (No answer given)
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