Use the Lagrange multiplier technique to find the maximum and minimum values of on the ellipse defined by the equations and , and where they occur

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Use the Lagrange multiplier technique to find the maximum and minimum values of on the ellipse defined by the equations and , and where they occur

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

what are the equations?
what is the function more importantly.
f(x,y,z)=x+z^2 g(x,y,z)=x^2+y^2 h(x,y,z)=2y+z

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Maximize f(x,y,z) subject to the restriction g and h?
actually i know how to solve
but are these g and h related or both different
yeah maximize with restriction g and h i think
I would let G(x,y,z) = ( x^2 + y^2 , 2y + z) where this our constrained set.
so now partial derivative of f(x)=lamba(g(x))
yes,
\[\frac{ part( f}{par( x,y,z)} = (\lambda_1, \lambda_2, \lambda_3)\frac{par G}{par (x,y,z)}\]
if its two dimensional we need to take only 1 lambda then why 3 for 3D?
I don't know rigorous you're calc 3 is. Do you need to prove that G is a compact set? and f is continuous, then by Extreme Value Theorem our max actually exists.
I don't know how you need 1 eigenvalue for 2. You need 2.
lambda was probably written as a vector.
and it had two components.
basically if you have 2D then partial f(x,y)=partial (lambda (g,y)) then slove for lambda and find x and y then we can get max or min
but here its 3D and i dont know how to solve this
Same business here.
your part(g)/part(x,yz) is going to be a matrix 3x3.
find its eigenvalues using characteristic polynomial
or however you find eigenvalues.
but here f(x,y,z)=lambda g(x,y,z)or f(x,y,z)=lambdah(x,y,z) how i beed to proceed
Yea so what we did was COMBINE our restrictions into one function lets say W(f(x,y,z), h(x,y,z)) Thats what I meant by capital G up there.
W(x,y,z) = ( x^2 + y^2 , 2y + z)
| 2x 2y 0 | | 0 2y 1 | | |
turns out to be our Part(W)/dx,y,z. We only need 2 lambdas in this case. The eigenvalues depend on the rank of our matrix.
even a derivative is technically a matrix, so you were right when you said you only needed one lambda
so we have par f(x,y,z) = (lambda1, lambda2) | 2x 2y 0 | | 0 2y 1 | is your linear algebra good enough to find lambdas?
ok i will try to solve and wil you be available online??
what do you get as partial f(x,y,z)
<1,0,2z>
<1,0,2z> = | 2x 2y 0 | | 0 2y 1 |
multiply the lambda through the matrix. then you should be able to pick out a linear system of equations. Use that to find lam1 and lam2
here 3 equations and 5 unknowns
Don't worry we are just trying to find expressions for x,y,z not explicit answers. what did you get?
i got lam1=1/2x 2y(lam1+lam2)=0 lam2=2z
try to get expressions for x, y,z and remember you can still use you're functions g, h
BTW, are you sure the functions weren't equal to anything?
no
g(x,y,z)=x^2+y^2 h(x,y,z)=2y+z These two can describe tons of functions.
x^2 + y^2 = 5, is certainly not the same as x^2 + y^2 = 10, and they will have max's in different points.
if i solve i got 2 points (1,0,0) and (-1,0,0) are these correct??
or are we doing a general case? set them equal to x^2 + y^2 = a 2y+z = b. How did you do that..
i solved the above equations with g(x) ,h(x)
x^2 + y^2 = 1 and 2y+z = 0 with the equations with lambdas
oh so they were equal to something.
COOL! i was getting scared.
am i doing correct or the points i got correct and the functional values at this point gives the value??
I hope so, don't make me do the algebra =P
x^2 + y^2 = 1 and 2y+z = 0 was this given?
yes

Not the answer you are looking for?

Search for more explanations.

Ask your own question