Find the critical points of the given function and then determine whether they are local maxima, local minima, or saddle points.
f (x, y) = x^2 + y^2 + 2xyf(x,y)=x 2 +y 2 +2xy

Answers

Answer 1

Answer:

[tex]y =-x[/tex] ---- critical point

local minima

Step-by-step explanation:

Given

[tex]f(x,y) = x^2 + y^2 + 2xy[/tex]

Required

Determine the critical point

Differentiate w.r.t x

[tex]f_x =2x + 2y[/tex]

Differentiate w.r.t y

[tex]f_y =2y + 2x[/tex]

Equate both to 0

[tex]2x + 2y =0[/tex]

[tex]2y =0-2x[/tex]

[tex]2y =-2x[/tex]

Divide by 2

[tex]y =-x[/tex] ----- in both equations

Hence:

The critical point is: [tex]y =-x[/tex]

Solving (b):

We have:

[tex]f_x =2x + 2y[/tex]

[tex]f_y =2y + 2x[/tex]

This is represented as:

[tex]D = \left[\begin{array}{cc}2&2\\2&2\end{array}\right][/tex]

Calculate the determinant

[tex]|D| =2 * 2 -2 * 2[/tex]

[tex]|D| = 4-4[/tex]

[tex]|D| = 0[/tex]

The critical point is at local minima


Related Questions

Choose the linear inequality that describes the graph the grey area represents the shaded region

Answers

Answer:

Explain to me how you expect anyone to do this,

as you haven't provided the graph or the inequalities.

Step-by-step explanation:

Помогите пожалуйста
y= sinx/cosx ; y=?

Answers

Answer:

[tex]\frac{1}{cos^2x}[/tex]

Step-by-step explanation:

[tex]y'=\frac{(sinx)'*cosx-(cosx)'*sinx}{cos^2x}=\frac{1}{cos^2x}.[/tex]

Can y’all help me on question 11?!

Answers

Answer:

The correct answer is choice C.

Step-by-step explanation:

To find the area of the arrow, we must add together the areas of the rectangle and the triangle that make up the arrow.  The rectangle has a length of 10 inches and a width of 4 inches, and the triangle has a base of 8 inches and a height of 2 inches.  Using this information, we can plug numbers into the following formula:

Area of arrow = area of rectangle + area of triangle

Area of arrow = (10*4)+(1/2*8*2)

Area of arrow = 40 inches squared + 8 inches squared

Area of arrow = 48 inches squared

Therefore, the correct answer is option C, 48 square units (in this case, inches).

Hope this helps!

In a group of students. 20 study Account. 21 Study mathematics 18 study history 7 study account only 10 study mathematics only 6 study account and mathematics only and 3 study mathematics and history only.how many student are there altogether

Answers

Answer:

In total there are 50 students.

Step-by-step explanation:

Since in a group of students 20 study account, 21 study mathematics, 18 study history, 7 study account only, 10 study mathematics only, 6 study account and mathematics only and 3 study mathematics and history only, to determine how many student are there altogether the following calculation must be performed:

7 + 10 + 6 + 3 = 26

Account = 20 - 7 - 6 = 7

Mathematics = 21 - 10 - 6 - 3 = 2

History = 18 - 3 = 15

26 + 7 + 2 + 15 = X

50 = X

Therefore, in total there are 50 students.

What is The sum of b and 11

Answers

B+11 ? I’m not sure is this high school math ?

Find the distance between the points (0, -3) and (4, 0).

A. 7
B. 1
C. 25
D. 5​

Answers

9514 1404 393

Answer:

  D.  5

Step-by-step explanation:

The distance formula is good for finding the distance between two points.

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((4 -0)² +(0 -(-3))²) = √(16 +9) = √25

  d = 5

The distance between the points is 5 units.

_____

You may notice that the line between the points makes a 3-4-5 right triangle with the coordinate axes.

8b - 5a + 4 for a = -4 and b = 7

If anyone gets this tysm

Answers

Answer:

80

Step-by-step explanation:

Given Question,

8b - 5a + 4

Given Values:

a = -4 and b = 7

Solution,

8(7) - 5(-4) + 4

= 56 + 20 + 4

= 80 (Ans)

Answer:

80

Step-by-step explanation:

8b - 5a + 4

a = - 4

b = 7

8(7) - 5(- 4) + 4

56 - (- 20) + 4

56 + 20 + 4

60 + 20

80

The summit of a volcano is 5 kilometers (km) above sea level, as shown below.
If the ocean floor has an elevation of -5 kilometers, which statement describes
the distance of the summit and the ocean floor?
It's not 0 or 5

Answers

Well 5 is -10 km away from -5. We can further prove this by adding -5 + 10, giving us 5. Answer is 10!

A. 40

B. 60

C. 140

D. 80

Answers

Answer:

measure of 4=360-(100+120)

=360-220

=140

so option C is the answer

Answer:

D. 80 is your answer

Step-by-step explanation:

If ∠6 is 120 and ∠5 is 100 we see a pattern forming for example, if we divide 120 by 6 we get 20 this is the same for if we divide 100 by 5, we get 20. Now all we need to do for ∠4 is to multiply it by 20 = 80, which is your answer!

Have a great day and I hope this helps!

Use the correct function to find the missing angle y measurement to the
nearest whole degree. Then using the checkboxes, select the function you
used, and the answer you found rounded to the nearest degree. (SELECT
2 ANSWERS - READ CAREFULLY) Work points are build into the results. *
18 in
yo
20 in.
Cos
Tan
64 degrees
Sin
42 degrees
26 degrees

Answers

Answer:

Cos;

26 degrees

Step-by-step explanation:

Recall: SOH CAH TOA

Reference angle = y°

Adjacent side = 18 in.

Hypotenuse = 20 in.

We would apply the trigonometric function CAH since we are dealing with the Adjacent side (A) and the Hypotenuse (H). Thus:

Cos y° = Adj/Hyp

Cos y° = 18/20

Cos y° = 0.9

y° = cos^{-1}(0.9)

y = 25.8419328° ≈ 26 degrees (nearest whole degree)

The answers are:

Cos and 26 degrees

!!!!!!!1I WILL GIFT YOU MANY POINTSSSSS

Answers

Answer:

The third one down

Step-by-step explanation:

m, Slope is negative

b, Y-intercept is positive

Help ASAP pls I will give brainlist

Answers

Answer:

Step-by-step explanation:

There is a issue here...

is the spotted blue section considered "a blue sector"?

Assuming that "blue" or "red" is only a solid blue or red, this is the answer...

1)  (1/10)* (3/10) = .03

2) (3/10) * (3/10) = 9/100 = .09

3) (3/10) * (1/10) = 3/100 = .03

4) (4/10) * (3/10) = 12/100 = .12

if the spotted blue and the solid blue are considered blue then this would be the result ...

1)  (1/10)* (3/10) = .03

2) (4/10) * (3/10) = 12/100 = .12

3) (3/10) * (1/10) = 3/100 = .03

4) (8/10) * (3/10) = 24/100 = .24

A group of 12 friends bought tickets for an afternoon concert. However, not all of the friends were able to sit together. Tickets for floor seats cost $15 each, and tickets for tier seats cost $70 each. The total cost of the tickets was $345. How many tickets for tier seats did they purchase

Answers

Answer:

3 tier seats tickets

Step-by-step explanation:

Let the friends that bought floor seats be x and let the friends that bought tier seats be y.

Thus;

x + y = 12 - - - (eq 1)

Floor seats tickets cost $15 each, and tier seats tickets cost $70 each. The total cost of the tickets was $345. Thus;

15x + 70y = 345 - - - (eq 2)

Let's make x the subject in eq (1)

x = 12 - y

Putting this for x in eq 2 gives;

15(12 - y) + 70y = 345

180 - 15y + 70y = 345

55y = 345 - 180

55y = 165

y = 165/55

y = 3

Put 3 for y in x = 12 - y to get;

x = 12 - 3

x = 9

Thus, they purchased 9 floor seats tickets and 3 tier seats tickets

Tasta's bank account was. She deposited a check into her bank account and her new total is. How much was the check that Tasta deposited into her account?

Answers

Answer:

Step-by-step explanation:

New Total equals Previous Total plus the Check value

New Total minus Previous Total   equals   the Check value

Her new total is  -  Tasta's bank account was = Check value

Rewrite the equation by completing the square.
4x² + 20r + 25 = 0
(x+...)^2=...

Answers

Answer:

The equation [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex] is equal to [tex]\left(x + \frac{5}{2} \right)^{2} = 0[/tex].

Step-by-step explanation:

Let be the equation [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex], we proceed to rewrite the equation solely by algebraic means:

1) [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex] Given

2) [tex](2\cdot x)^{2} + 10\cdot (2\cdot x) + 25 = 0[/tex] Definition of power/Associative property

3) [tex](2\cdot x + 5)^{2} = 0[/tex]   Perfect square trinomial

4) [tex]2^{2}\cdot \left(x + \frac{5}{2} \right)^{2} = 0[/tex] Distributive property/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]

5) [tex]4\cdot (x + \frac{5}{2} )^{2} = 0[/tex] Definition of power

6) [tex]\left(x + \frac{5}{2} \right)^{2} = 0[/tex] Compatibility with multiplication/Commutative and modulative properties/[tex]a\cdot 0 = 0[/tex]

A bag holds 20 red marbles and 40 green ones, for a total of 60 marbles. Ryan picks one marble from the bag at random, hoping to pick a red marble. Which of the following statements is true?
a. The probability that Ryan will pick a red marble on the first try is 67%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.
b. The probability that Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.
c. The probability that Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.
d. The probability that Ryan will pick a red marble on the first try is 67%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.

Answers

Answer:

C

Step-by-step explanation:

The probability Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, that % will decrease.

The probability of picking a red marble on the first try is 33%, and if Ryan keeps this marble and picks another from the bag, the probability of picking a green marble decreases.

Thus, option (C) is correct.

In this case, there are 20 red marbles out of a total of 60 marbles.

So the probability of picking a red marble on the first try is 20/60, which simplifies to 1/3 or 33%.

If Ryan keeps the red marble and picks another one from the bag, the total number of marbles becomes 59.

The number of green marbles remains the same at 40.

Therefore, the probability of picking a green marble on the second try is 40/59, which is less than the probability of picking a green marble on the first try.

Hence, the probability of picking a red marble on the first try is 33%.

Thus, option (C) is correct.

Learn more about Probability here:

brainly.com/question/32117953

#SPJ4

for what values of x are these functions defined x - 1

Answers

Answer:

The function is defined for all real numbers.

which can be denoted as >> R


find the slope of the graph

Answers

Answer:

We count across to 4 on y axis = 2

and count down from 4 to  -2 on x axis = -6

-6/2 = -3

m = -3

We know its minus because the reciprocal is the perpendicular imaginary line and if -3 is for the descending line then any ascending perpendicular line would show m = -1/-3 = 3

Step-by-step explanation:

M=-3 . The rise over run is 3/1 which is simplified as just 3. Since the line is leaning towards the left, the slope is negative.

please help! (listing BRAINLIST and giving points) ​:D​

Answers

Answer:

x = 50 + 95 = 145

.........

Answer:

x = 145°

Step-by-step explanation:

Given,

Measure of the first angle = 50°

Measure of the second angle = 95°

We know,

Sum of 3 angles of a triangle is equals to 180°

∴ The third angle = 180° - (50+95)°

                             = 180° - 145°

                             = 35°

Again,

Straight angle = 180°

∴ x = 180° - 35°

      = 145°

∴x = 145°

Sydney is cutting the crust from the edges of her sandwich. The dimensions, in centimeters, of the sandwich is shown.

Answers

I can’t see the format it’s not showing up

Answer:

The answer is B) x = 8x² + 34; 45.52 centemiters

Step-by-step explanation:

WILL MARK BRAINLIEST PLEASE HELP

a survey of boys and girls in second grade was conducted asking whether or not they like pizza. The partially completed two-way table shows results of the survey. How many boys were included in the survey?

Answers

64-35= 29

so there were 29 boys included in the survey

Step-by-step explanation:

answer is in the above photo

there are 29 boys total

An angle whose measure is - 102° is in standard position in which quadrant does the terminal side of the angle fall?
O Quadrant
O Quadrant il
Quadrant III
O Quadrant IV

Answers

It would fall in Quadrant III

Which of the following is equal to the rational expression
below when x+2 or 9?
4(x - 2)
(x - 2)(x-9)

Answers

Answer:4/x-9

Step-by-step explanation:

what are the domain and range of this function

Answers

Answer:

The domain is all real numbers

The range is y ≥ -8

Step-by-step explanation:

The domain is the values that x can take

The domain is all real numbers

The range is the values that y can take

The range is y ≥ -8

Destiny has borrowed $8 from 7 different friends. Write an integer that
represents Destiny's total debt to her friends.

Answers

Answer:

56

Step-by-step explanation:

7×8=56

Hope this helps! :)

what are the two types of probability​

Answers

Answer:

The two "types of probability" are: 1) interpretation by ratios, classical interpretation; interpretation by success, frequentist interpretation. The third one is called subjective interpretation.

HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

No solution

Step-by-step explanation:

Given

[tex]|x| = -1[/tex]

Required

The solution

The above equation has no solution.

This is because [tex]|x| \ge 0[/tex]

In otherwords, the absolute value of a number is always positive.

help answer please help

Answers

I think the answer is frequency table, but I’m not sure.. make your best guess or try asking other people.

Answer:

The best was to display a set of data with a wide range would be

a histogram.

Step-by-step explanation:

It's a graphical display of bars which will help you measure the central tendency.

There are approximately 1.2×10 to the eighth household in the US if the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day

Answers

Answer:

[tex]Total = 4.8 * 10^{10}[/tex]

Step-by-step explanation:

Given

[tex]h = 1.2 * 10^8[/tex] --- households

[tex]g = 400[/tex] --- gallons

Required

The number of households

To do this, we simply multiply the average households by the gallons.

[tex]Total = g* h[/tex]

[tex]Total = 400 * 1.2 * 10^8[/tex]

[tex]Total = 480 * 10^8[/tex]

Rewrite as:

[tex]Total = 4.8 * 10^2 * 10^8[/tex]

[tex]Total = 4.8 * 10^{10}[/tex]

Solve the inequality −14z<−37, and write the solution in interval notation.

Answers

Answer:

z is greater than 27/14

z € ( 37/14 ∞)

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