.Does the function
f(x,y) = x^2/2 + 5y^3 + 6y^2 − 7x
have a global maximum and global minimum? If it does, identify the value of the maximum and minimum. If it does not, be sure that you are able to explain why.
Global maximum?
Global minimum?

Answers

Answer 1

The function f(x,y) = x^2/2 + 5y^3 + 6y^2 − 7x has a global maximum at (7,-4/5) and no global minimum.

To determine if the function has a global maximum or minimum, we need to check its critical points and boundary points.

Taking partial derivatives with respect to x and y and setting them equal to 0, we have:

∂f/∂x = x - 7 = 0

∂f/∂y = 15y^2 + 12y = 0

From the first equation, we get x = 7. Substituting this into the second equation, we get:

15y^2 + 12y = 0

3y(5y + 4) = 0

This gives us two critical points: (7, 0) and (7, -4/5).

To check if these critical points are local maxima or minima, we need to use the second partial derivative test. Taking second partial derivatives, we have:

∂^2f/∂x^2 = 1, ∂^2f/∂y^2 = 30y + 12

∂^2f/∂x∂y = 0 = ∂^2f/∂y∂x

At (7,0), we have ∂^2f/∂x^2 = 1 and ∂^2f/∂y^2 = 0, which indicates a saddle point.

At (7,-4/5), we have ∂^2f/∂x^2 = 1 and ∂^2f/∂y^2 = -12, which indicates a local maximum.

To check for global extrema, we also need to consider the boundary of the domain. However, the function is defined for all values of x and y, so there is no boundary to consider.

Therefore, the function has a global maximum at (7,-4/5) and no global minimum.

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Related Questions

someone solve please

Answers

24.75 yard²

Mark me as brainlist

Using properties of logarithms in excersises 13-18, use the properties of logarithms o write the logarithm in terms of log3(5) and log3(7) log3 (21/5)

Answers

Answer:

[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]

Step-by-step explanation:

Given

[tex]log_3(\frac{21}{5})[/tex]

Required

Express in terms of [tex]log_3(5)[/tex] and [tex]log_3(7)[/tex]

[tex]log_3(\frac{21}{5})[/tex]

Express 21 as 7 * 3

[tex]log_3(\frac{21}{5}) = log_3(\frac{7 * 3}{5})[/tex]

Apply law of logarithm

[tex]log_3(\frac{21}{5}) = log_3(7) + log_3(3) - log_3(5)[/tex]

[tex]log_3(3) = 1[/tex]. So, we have:

[tex]log_3(\frac{21}{5}) = log_3(7) + 1 - log_3(5)[/tex]

Rewrite:

[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]

A rectangular lettuce patch, 560 square feet in area, is to be fenced off against rabbits. Find the least amount of fencing required if one side of the land is already protected by a barn. What are the dimensions?

Answers

Oh yeah sweetie no lol just called and him he told him to tell me that you

The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft

Let x represent the length of the fence and y represent the width of the fence.

Since the area is 560 square feet, hence:

Area = length * width

560 = xy

y = 560/x

One side of the land is already protected by a barn, hence:

Perimeter (P) = x + x + y = 2x + y

P = 2x + y

P = 2x + 560/x

For least amount of fencing, dP/dx = 0, hence:

dP/dx = 2 - 560/x²

0 = 2 - 560/x²

560/x² = 2

2x² = 560

x = 16.7

y = 560/16.7 = 33.5 ft

The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft

Find out more at: https://brainly.com/question/10415523

Mr. Alvarez makes a walkway of 3 cement slabs.He uses 14 cubic feet of cement to make the walkway.Each square slab has a volume of 4 cubic feet

Answers

Answer:

I suppose that you want to see how we can find the volume of each individual slab with the given information, the procedure is as follows.

The walkway has 3 cement slabs,

He uses a total amount of 14 cubic feet to make the complete walkway.

This means that the 3 cement slabs together have a total volume of 14 ft^3

To find the volume of each slab, we need to find the quotient between the total volume and the total number of slabs, then we get:

Volume of each slab = (14 ft^3)/3 = 4 ft^3

This means that each cement slab has a volume of 4 ft^3.

Answer:

6 ft^3

Step-by-step explanation:

James has 838 feet of rope. There are 17 teams of hikers. If James gives an equal amount of rope to each team, how much rope will each team receive?

Answers

Answer:

838 ÷ 17 = 49.29 feet each

Step-by-step explanation:

divide the total rope by number of hikers equals amount of rope each hiker will receive.

What statement describes the expression 10 +1/4× (5+3)-3

Answers

Answer:

The answer would be 9.

Step-by-step explanation:

10 + 1/4 x (5 + 3) - 3

10 + 1/4 x (8) - 3

10 + 2 - 3

12 - 3

9

17.
Is the relation a function? Why or why not?
{(–8, –4), (–2, 0), (1, 3), (–2, 6)}

A. Yes; only one range value exists for each domain value.

B. No; the relation passes the vertical line test.

C. No; two range values exist for domain value –2.

D. Yes; two range values exist for domain value –2.

Answers

Answer:

C. No; two range values exist for domain value –2.

Step-by-step explanation:

The relation is not a function.

The -2 in the domain repeats

Since  

x

=

2

produces  

y

=

0

and  

y

=

6

, the relation  

(

8

,

4

)

,

(

2

,

0

)

,

(

1

,

3

)

,

(

2

,

6

)

is not a function.

The relation is not a function.

cuantas combinaciones de 5 cifras se pueden hacer con los sig numeros 1,2,3,4,5

Answers

Responder:

Hay 120 combinaciones posibles

[tex]4x\leq 12[/tex]

Answers

Divide each term by  

4

and simplify.

Inequality Form:

r ≤ 3

Interval Notation:

( − ∞ , 3 ]

Hope this helps!!! Lol

I need help with a/d​

Answers

what’s the question asking??

Answer:

yeah whats the question asking >:(

You have a friendship club. There are 12 members in your club. On the twelfth day of each month, you have a friendship call. Each member of the club talks to every other member that day by phone. This way everybody expresses his or her friendship with each other. How many conversations are made on that day?

Answers

Answer: There are a total of 66 conversations.

Step-by-step explanation:

Ok, we have 12 members.

let's call them:

member 1, member 2, member 3, etc...

Let's assume that member 1 starts talking to the others, then he talks to:

member 2, member 3, member 4, etc.

So member 1 talks to the other 11 members.

We have already 11 conversations.

Now let's count the conversations of member 2.

He talks to member 1, member 3, etc.

But the conversation between member 1 and member 2 was already counted, so we do not count it this time, then here we have other 10 conversations.

now for member 3. He talks with member 1, member 2, member 4, member 5, etc...

But conversations between member 1 and member 3, and member 2 and member 3 are already counted, so here we have 9 new conversations.

We already can see the pattern here.

For each new member that we count, the number of conversations is one less than for the previous member.

The total number of conversations will be:

11 + 10 + 9 + 8+ 7 + 6+5 + 4 + 3+ 2+ 1 = 66

Sari wrote the equivalent ratios below to convert cups to fluid ounces. How many fluid oz. Are in 9 cups.

Answers

Answer:

the  number of fluids ounces in 9 cups is 72 fluid ounces

Step-by-step explanation:

The computation of the number of fluids ounces in 9 cups is shown below:

As we know that

In 1 cup = 8 fluid ounces

So for 9 cup it is

= 9 × 8

= 72 fluid ounces

hence, the  number of fluids ounces in 9 cups is 72 fluid ounces

I need help with math if you don't know the answer get out of the question and don't answer it and give the wrong answer or some link or even say "I don't know" or anything like that it's not fair to me cause it a waste of my points I will report your if you do that :) have a nice day and stay safe

Answers

Answer:

1.5 or 1 1/2 pounds of candy

Step-by-step explanation:

First, divide 2 into 4 equal pieces. You do this because of the denominator in 3/4.

2 divided by 4= 0.5

Then 0.5 times 3 because of the numerator in 3/4.

0.5 times 3= 1.5

You can convert this into the fraction 1 1/2 or you can leave it a 1.5

Hope this helps!

These two figures are the image and pre-image of a
dilation.
Find the value of x.
4 m
6 m
4 m
6 m
8 m
9 m
6 m

Answers

Answer:

4m i think it sounds about right

Answer: the answer is 9m or D

Step-by-step explanation:

What is the value of 6(2b-4) when b=5?

Answers

Answer:

126

Step-by-step explanation:

Step-by-step explanation:

When b = 5 Then

6( 2b - 4)

= 6 ( 2 *5 - 4)

= 6 ( 10 - 4)

= 6 * 6

= 36

Hope it will help :)

Find the value of x. Round to the nearest tenth:

Answers

Answer:

x = 13.5

Step-by-step explanation:

help please
4 − ( −12) + ( −7) =​

Answers

............................................9


Each letter in the word "TEXTBOOK" is written on an identical tile and placed in a bag. What is the probability of
drawing a vowel on the first try?

Answers

Answer:

37.5% or 3/8

Step-by-step explanation:

There are 8 total letters, and only 3 vowels, which can be the fraction 3/8. 3/8 as a percent is 37.5%. Hope this helps!

Answer:

Capital letters and Rotations marks

Enumere Cuatro Fuentes de Corriente continua​

Answers

Answer:

La corriente continua es producida por fuentes como baterías, termopares, celdas solares y máquinas eléctricas de tipo conmutador de tipo dínamo. La corriente continua puede fluir en un conductor como un cable, pero también puede fluir a través de semiconductores, aislantes o incluso a través de un vacío como en los haces de electrones o iones. espero que esto te ayude

Convert the following quadratic equation to vertex form. 2) 3x2 - 12x - 5

Answers

Answer:

3(x - 2)² - 17

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Using the method of completing the square.

Given

3x² - 12x - 5 ← factor out 3 from the first 2 terms

= 3(x² - 4x) - 5

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² - 4x

= 3(x² + 2(- 2)x + 4 - 4 ) - 5

= 3(x - 2)² - 12 - 5

= 3(x - 2)² - 17 ← in vertex form

Last season, Patrick Mahomes threw for 4,800 yards in 16 games. This season, he had a 15% increase in the number of yards he threw per game.

How many yards did he throw per game after the increase?

Answers

Answer:

345 yards.

Step-by-step explanation:

4800/16 = 300

300 increase 15% =

300 × (1 + 15%) = 300 × (1 + 0.15) = 345

Which of the following are properties of the circumcenter of a triangle? Check
all that apply.
A. The circumcenter is at the intersection of the perpendicular
bisectors of the triangle's sides.
B. The circumcenter of an obtuse triangle is always outside it.
M C. The circumcenter is equidistant from each vertex of the triangle.
D. The circumcenter is equidistant from each side of the triangle.

Answers

Answer: A. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.

C. The circumcenter is equidistant fromeach vertex of the triangle.

D. The circumcenter is equidistant from each side of the triangle.

Step-by-step explanation:

The properties of the circumcenter of a triangle from the options given include:

• The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.

• The circumcenter is equidistant fromeach vertex of the triangle.

• The circumcenter is equidistant from each side of the triangle.

Option B is wrong as the circumcenter of an obtuse triangle is not always outside it. For the circumcenter, there is intersection of all the three lines and it's not important that they should always be outside.

What is an equation of the line that passes through the points (-1,3) and (-1,6)

Answers

Answer:

x=-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)=(6-3)/(-1-(-1)=3/(-1+1)=3/0

your slope is undefined.

x=-1

Solve the equation.
5x = 3x²+1
5+ 13
a
5-√13
c.
-5+ √13
5- V13
X=
or
or
12
12
6
6
b.
-5+ √13
5-√3
d.
S+~13
5- 13
Of
12
or
12
6
6

Answers

Answer: x = 5+√13/6, 5-√13/6
Hope this helps

The width A rectangle is 3 cm less then its length. The perimeter of the rectangle is 30 CM. Find The length and width of the rectangle

Answers

w = l - 3

w = 9 - 3

w = 6

//

l = 9

w = 6

//

p = 2(9) + 2(6)

p = 30


What is the area of the triangle?
6 square inches
18 square inches
12 square inches
30 square inches

Answers

Answer:

6 square inches.

Explanation:

You should use 4 for the base and 3. If you used the formula to find the area of the triangle, then you should get 6 for your answer.

Answer:

answer is 6.

Step-by-step explanation:

the base as 4 in. times the height as 3in. divided by 2= 6in.

A pelican has a wingspan of 8 feet.
An eagle has a wingspan of 6 feet.
How much longer is the wingspan
of a pelican?

Answers

Answer:

I'm pretty sure the answer would be 2 feet.

Step-by-step explanation:

8-6=2

Given the function below, what is the g(-8)?

g(x)=2x+1

Answers

the answer is -15 because you insert the -8 where the x goes.

In ΔTUV, t = 410 cm, ∠U=27° and ∠V=78°. Find the length of v, to the nearest 10th of a centimeter.=

Answers

Answer: 415.2

Step-by-step explanation:

please help me out with this​

Answers

6m (m+2) = 0 is the factored form
m=0, m=-2 is m

Steps are on paper
If you need more explanation, comment
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