1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Darina [25.2K]
3 years ago
6

Identify any extrema of the function by recognizing its given form or its form after completing the square. Verify your results

by using the partial derivatives to locate any critical points and test for relative extrema.
g(x, y) = 5 - (x - 3)² - (y + 2)²
Mathematics
1 answer:
Andrews [41]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that,

g(x, y) = 5 - (x - 3)² - (y + 2)²

Let find the grad of the function,

The grad of a function is defined as

∇g= ∂g/∂x •i + ∂g/∂y •j + ∂g/∂z •k

∇g = gx•i + gy•j + gz•k

gx = -2(x-3) = -2x+6

gy = -2(y+2) = -2y -4

∇g = (-2x+6) •i + (-2y-4)•j

We have a maximum or a minimum If g conservative, then, ∇g = 0i +0j

Then comparing this to the grad of the function

(-2x+6) •i + (-2y-4)•j = 0i +0j

Then, -2x+6 = 0

2x=6

x = 3

Also, -2y-4=0

-2y=4

y = -2

Then, g(x, y) = 5 - (x - 3)² - (y + 2)²

g(x, y) = 5 - (3 - 3)² - (-2 + 2)²

g(x, y) = 5

So the critical point is (3, -2, 5)

gx =-2x+6

Second derivative of gx with respect to x

gxx=-2

gy=-2y-4

Second derivative of gy with respect to y

gyy=-2

Second derivative of gx with respect to y

gxy =0

d =gxxgyy - (gxy)²

Then, gyy=gxx

d = -2×-2 -0²

d = 4-0=4

Since d>0

Since d is greater than 0, then, it is not a chair points.

Then, since gxx=-2<0, gyy=-2<0

Cause the second derivative in x (or in y) is less than zero, then the point is relatively maximum

So the maximum point is (3, -2, 5).

You might be interested in
Kevin and his children went into a restaurant and he bought $31.50 worth of hotdogs and drinks. Each hotdog costs $4.50 and each
stich3 [128]

Answer:

<em>He bought 6 hotdogs and 2 drinks</em>

Step-by-step explanation:

<u>System of Equations</u>

Kevin and his children went into a restaurant and bought $31.50 worth of hotdogs and drinks. Each hotdog costs $4.50 and each drink costs $2.25.

To solve the system of equations, we'll call the variables:

x = number of hotdogs

y = number of drinks

The first condition yields the equation:

4.50x + 2.25y = 31.50          [1]

It's also known he bought 3 times as many hotdogs as drinks, thus:

x = 3y         [2}

Substituting [2] in [1]:

4.50(3y) + 2.25y = 31.50

Operating:

13.5y + 2.25y = 31.50

15.75y = 31.50

y = 31.50/15.75

y = 2

And

x = 3*2 = 6

He bought 6 hotdogs and 2 drinks

5 0
3 years ago
How does rewriting the mixed numbers as whole numbers and fractions make it easier to multiply?
bixtya [17]

Answer:

A

Step-by-step explanation:

3 0
3 years ago
A Bag of Halloween Candy weighs 4.7 pounds, how much would 3.4 bags weigh
lyudmila [28]
You could multiply the two numbers to get a product of 15.98 pounds.
7 0
3 years ago
HURRRRRRYYYYYYY 1 QUESTION EXPERTS/ACE HELP QUICK!!!!!
Tomtit [17]
I believe the answer is 275 miles. Hope this helps!
8 0
3 years ago
Read 2 more answers
3. Given AB with coordinates A(-4,5) and B(12,13). Find the horizontal distance and the vertical
SCORPION-xisa [38]

The required distance would be 17.88 units coordinates A(-4,5) and B(12,13) and the horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.

<h3>What is the distance between two points?</h3>

The distance between two points is defined as the length of the line segment between two places representing their distance.

Given AB with coordinates A(-4,5) and B(12,13).

The formula of the distance between two points is A(x₁, y₁) and B(x₂, y₂) is given by: d (A, B) = √ (x₂ – x₁)² + (y₂ – y₁) ².

x₁ = -4, y₁ = 5

x₂ = 12, y₂ = 13

distance = √ (12 – (-4))² + (13 – 5)²

distance = √ (12 + 4)² + (8)²

distance = √ (16)² + (8)²

distance = √ (256 + 64)

distance = √320

distance = 17.88 units

The horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.

Learn more about the distance between two points here:

brainly.com/question/15958176

#SPJ1

6 0
1 year ago
Other questions:
  • Need some help please!
    13·1 answer
  • A fruit punch recipe calls for 18 cups of soda and 6 cups of grape juice.
    15·1 answer
  • Help please asap thanks​
    15·1 answer
  • Could you please help me out I think that answer is c
    11·1 answer
  • Round to nearest tenth 8 divided by 6.403
    11·2 answers
  • On a true/false test, the ratio of true questions to false questions is 3 to 7. What is the ratio of true questions to total que
    11·2 answers
  • What is the equation in slope-intercept form of a line that is parallel to y=−3x+1 and passes through the point (3, 2)? Enter yo
    15·2 answers
  • What is 1/4 divided by 4
    13·1 answer
  • Solve for X. 3/4x+7/8=4 1/4 Enter your answer as a mixed number in simplest form in the box.
    15·1 answer
  • A piece of paper is 10 1 2inches long. If you put 3 2inch sticky notes end to end across the length of the paper, how many stick
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!