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
1. A raffle prize of 14x^2/15 dollars is to be divided among 7x people. Write an expression for the amount of money that each pe
kvasek [131]

Step-by-step explanation:

Q1

7x people=14x^2/15

1 person= (14x^2/15)÷7x

// =(7x^2/15)÷x

Each person will recieve= (7x^2/15)÷x

7 0
3 years ago
7 (8.5 minus 1.5) + 8 divided by 2
erica [24]

Answer:

eetf fee

Step-by-step explanation:

yyff gf gg gfdf jhdsd tdef gsseig fetygc seeyug. eyyyfvdeetg. dthgd fssergg

5 0
3 years ago
Factor 3x + 9<br><br> Please explain how you got the answer
eimsori [14]

To factor 3x + 9 you should know that 3 is a common factor of both 3 and 9, so you can factor 3 out in both numbers like this.

3x + 9

3(x + 3)

When you factor out 3 on both numbers you should know that 3 X 3 = 9 and since you factored out 3 there would be another 3 left so you would have the answer: 3(x + 3)

Here is another equation that might help:

24x + 36

Since 12 is a common factor of both numbers, factor 12 out of the equation:

12 (2x + 3)

You know that 12 x 2 = 24 and that 12 x 3 = 36

And since you can't factor out anymore numbers because 2 and 3 doesn't have any common factors with each other you get the answer:

12 (2x + 3)


3 0
3 years ago
Mr liston bought lunch for $ 12.80. He gave the waiter a tip of 15 %. How much money did the waiter recieve?
Serga [27]
The answer would be B, because 12.80 times .15 is 1.92
5 0
3 years ago
Read 2 more answers
En la fábrica de Don Toño hoy fabricaron 320 pantalones, si los guardan en cajas donde caben 50 ¿cuántas cajas llenaron?
Scrat [10]

Answer:

6.4 Cajas

Step-by-step explanation:

320/50 = 6.4 Cajas

8 0
3 years ago
Other questions:
  • A construction company is digging a hole for a swimming pool. The hole will be 12 yards long, 7 yards wide, and 3 yards deep. Ho
    14·1 answer
  • In how many distinct ways can the letters in engineering be arranged?
    8·2 answers
  • Which value of x makes the equation true? x – 18.7 = –12
    15·1 answer
  • In 2010,85% of the ratings for 1618 video games were E ( for everyone).how many video games received the E rating ?
    9·1 answer
  • Evaluate 4m+23+np−3, when m=7, n=2, and p=8.
    13·2 answers
  • The coordinate pairs could represent the the vertices of a triangles congruent to KLM?
    8·2 answers
  • Answer correctly for brainliest do not send pdfs or links
    7·2 answers
  • For each geometric sequence, write a recursive rupe by finding the common ratio by calculating the ratio of consecutive terms. W
    11·1 answer
  • What is the supplementary angle of 91.1 drgrees​
    12·1 answer
  • -2x^2+bx -5 Determine the b-value that would ensure the function has two real root.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!