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
Setler [38]
3 years ago
13

Use Lagrange multipliers to find the maximum and minimum values of

Mathematics
1 answer:
marusya05 [52]3 years ago
5 0

The Lagrangian is

L(x,y,\lambda)=x+8y+\lambda(x^2+y^2-4)

It has critical points where the first order derivatives vanish:

L_x=1+2\lambda x=0\implies\lambda=-\dfrac1{2x}

L_y=8+2\lambda y=0\implies\lambda=-\dfrac4y

L_\lambda=x^2+y^2-4=0

From the first two equations we get

-\dfrac1{2x}=-\dfrac4y\implies y=8x

Then

x^2+y^2=65x^2=4\implies x=\pm\dfrac2{\sqrt{65}}\implies y=\pm\dfrac{16}{\sqrt{65}}

At these critical points, we have

f\left(\dfrac2{\sqrt{65}},\dfrac{16}{\sqrt{65}}\right)=2\sqrt{65}\approx16.125 (maximum)

f\left(-\dfrac2{\sqrt{65}},-\dfrac{16}{\sqrt{65}}\right)=-2\sqrt{65}\approx-16.125 (minimum)

You might be interested in
What two numbers are the absolute value of 4
kati45 [8]
The absolute value is the distance from 0, so it would be 4 and -4
5 0
2 years ago
Read 2 more answers
How do you simplify 4/20
Anna71 [15]
\sf \frac{4}{20}~\underrightarrow{\sf ~simplify~by~4~~}~\frac{4:4}{20:4} =\boxed{\sf  \frac{1}{5} }
3 0
3 years ago
Read 2 more answers
What are 3 consecutive numbers that is the sum of -27.please be right.use odd numbers
qaws [65]
You're asking for three consecutive odd numbers, then
Let, the numbers = x, x+2, x+4

It is given that, x + x+2+ x+4 = -27
3x + 6 = -27
3x = -27 - 6
x = -33/3
x = -11
Then, x+2 = -9 & x+4 = -7

In short, Your Numbers would be: -7, -9,-11

Hope this helps!
6 0
2 years ago
Use the vertical line test to determine whether the graph shown to the right is the graph of a function
Andreas93 [3]

That's not a function.

Since a vertical line hits the graph more than once, if fails the test. (See graph below)

If it is a function, any vertical line you draw can only hit the graph once.

3 0
3 years ago
What is 280 million in scientific notation 
Phantasy [73]
The rule of scientifinc notation is that we can use number between 0 and 10, so here we can use 2.8. Lets do this
280 000 000 = 2.8 * 100 * 1 000 000
Now we can just multiply 2.8 by 10 to the power of number of 0 reapeted
So 2.8*10^8 - its the result
3 0
3 years ago
Other questions:
  • Michael is finding the area of parallelogram ABCD. To do
    10·2 answers
  • He was just up with me the sum of three consecutive numbers is 41 less than five times the largest number find the largest numbe
    5·1 answer
  • Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each sale
    8·1 answer
  • 67-78+26+39×2 answer thy question brothers im none smart
    11·2 answers
  • Elijah and Tyler, two high school juniors, conducted a survey on 13 students at their school, asking the students whether they w
    10·1 answer
  • Look at image i need help
    10·1 answer
  • Which of the following best describes the relationship between (x - 2) and the
    5·1 answer
  • What is the absolute value of -62/3
    12·1 answer
  • Chicago has an elevation of 991 feet above sea level. The elevation of Detriot is -923
    5·1 answer
  • The coordinates of the vertices of AHKM are H(3, -2),
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!