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2 years ago

6

Lenore needs an apartment immediately. She

1 answer:

AveGali [126]2 years ago

6 0

Not enough data given here. Incomplete question.

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(a)5%)Let fx, y) = x^4 + y^4 - 4xy + 1. and classify each critical point Find all critical points of fx,y) as a local minimum, l

lara31 [8.8K]

$f(x,y)=x^4+y^4-4xy+1$

has critical points wherever the partial derivatives vanish:

$f_x=4x^3-4y=0\implies x^3=y$

$f_y=4y^3-4x=0\implies y^3=x$

Then

$x^3=y\implies x^9=x\implies x(x^8-1)=0\implies x=0\text{ or }x=\pm1$

If $x=0$ , then $y=0$ ; critical point at (0, 0)
If $x=1$ , then $y=1$ ; critical point at (1, 1)
If $x=-1$ , then $y=-1$ ; critical point at (-1, -1)

$f(x,y)$ has Hessian matrix

$H(x,y)=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}$

with determinant

$\det H(x,y)=144x^2y^2-16$

At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
At (1, 1), the determinant is 128, and $f_{xx}(1,1)=12$ , which indicates a local minimum.
At (-1, -1), the determinant is again 128, and $f_{xx}(-1,-1)=12$ , which indicates another local minimum.

4 0

3 years ago

WILL GIVE BRAINLIEST<br> Subtract 9x^2+7x-2<br> from 8x-10

konstantin123 [22]

Answer:

x − 9 x ^2 − 8

Step-by-step explanation:

6 0

2 years ago

What is the volume of this sphere?

Darina [25.2K]

Answer:

523.59 or 523.60

Step-by-step explanation:

Volume for a sphere: 4/3πr^3 (4÷3x π x r ^ 3)

(r is radius, V is volume)

V= 4/3 x π x r^3

The diameter is 10, so the radius is 5...

V= 4/3 x π x 5^3

V= 4/3 x π x 125

CALCULATER: 4 ÷ 3 x π x 125

Answer 523.59 (523.60 rounded)

6 0

3 years ago

Solve for angle Z please help!!!!

bagirrra123 [75]

180 - 106 = 74

180 - 68 - 74 = 38

5 0

3 years ago

Read 2 more answers

Please help !! Correct and first answer I’ll give you brainesttttt ! What is the equation of the line?

jasenka [17]

Step-by-step explanation:

can u give image PlZzzzz ....

7 0

3 years ago

Read 2 more answers