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3 years ago

HELP PLEASEEEEEEE WILL MARK YOU AS BRAINLEIST

Mathematics

1 answer:

slamgirl [31]3 years ago

7 0

Answer:

-1, -1

Step-by-step explanation:

when you turn it it will change the coordinates as well

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Example 3 find the local maximum and minimum values and saddle points of f(x, y) = x4 + y4 − 4xy + 1. solution we first locate t

allsm [11]

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

$\begin{cases}f_x=4x^3-4y\\f_y=4y^3-4x\end{cases}$

We have critical points whenever both partial derivatives vanish:

$4x^3-4y=0\implies x^3=y\implies x=y^{1/3}$
$4y^3-4x=0\implies y^3=x=y^{1/3}\implies y^6=y\implies y=0,y=-1,y=1$
$\begin{cases}y=0\implies x=0\\y=-1\implies x=-1\\y=1\implies x=1\end{cases}$

The Hessian is

$\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}$
$\det\mathbf H(x,y)=(12xy)^2-16$

At (0,0), we have $\det\mathbf H(0,0)=-16$ , so (0,0) is a saddle point.

At (-1, -1), we have $\det\mathbf H(-1,-1)=128>0$ and $f_{xx}(-1,-1)=12>0$ , so (-1, -1) is a local minimum.

At (1, 1), we have $\det\mathbf H(1,1)=128>0$ and $f_{xx}(1,1)=12>0$ , so (1, 1) is also a local minimum.

3 0

3 years ago

What is the greatest common factor of 24s3,12s4, and 18s

ioda

The only number all of these numbers can be divided by is 2. Therefore, the GCF is 2

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4 years ago

Read 2 more answers

When a figure is translated on the coordinate plane you should add or subtract x and y? Is this statement true or false?

Sonja [21]

Answer: i think its true

Step-by-step explanation:

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3 years ago

In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and m

jenyasd209 [6]

Answer:

Step-by-step explanation:

since it's multiplication the largest result is the largest integer you have times the second largest integer you have(or itself but not in this case) and the smallest result is the smallest integer you have times the second smallest integer.

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Use the image above to identify and explain the relationship between the segments and circles A and B. In your explanation, be s

kykrilka [37]

Answer:

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Step-by-step explanation:

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4 years ago