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3 years ago

6

Slope 9/5 and this line is passing through ( 0,5)

1 answer:

Law Incorporation [45]3 years ago

4 0

Answer:

uuuujjjjj

Step-by-step explanation:

nnnnnnnnnnnnnñbbbbbbb

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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

Plz help me with this question thanks

Verizon [17]

Answer:

Y8

Step-by-step explanation:

7 0

3 years ago

What multiplies to -10000 and adds up to 0?

aleksley [76]

1
Vhvixr6
dtidtu
dtudtu
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5 0

4 years ago

Read 2 more answers

-8(3 - 4v) + 8v = 9v + 3 what is the answer?

gavmur [86]

Answer:

My sister and her sister and my mom are so adorable I love her and

Step-by-step explanation: was the name wrong I was talking to him about it haha is that a little

Kidsss was a great night out and this is what I

4 0

3 years ago

3. Consider the sequence,-8, -5, -2, 1, ...

Naddik [55]

Answer:

a) $a_n=3\,n-11$

b) $a_{20}=49$

c) term number 17 is the one that gives a value of 40

Step-by-step explanation:

a)

The sequence seems to be arithmetic, and with common difference d = 3.

Notice that when you add 3 units to the first term (-80, you get :

-8 + 3 = -5

and then -5 + 3 = -2 which is the third term.

Then, we can use the general form for the nth term of an arithmetic sequence to find its simplified form:

$a_n=a_1+(n-1)\,d$

That in our case would give:

$a_n=-8+(n-1)\,(3)\\a_n=-8+3\,n-3\\a_n=3n-11$

b)

Therefore, the term number 20 can be calculated from it:

$a_{20}=3\,(20)-11=60-11=49$

c) in order to find which term renders 20, we use the general form we found in step a):

$a_n=3\,n-11\\40=3\,n-11\\40+11=3\,n\\51=3\,n\\n=\frac{51}{3} =17$

so term number 17 is the one that renders a value of 40

5 0

3 years ago