Question

We will find the maximum and minimum values of f(x, y) = xy on the ellipse...

We will find the maximum and minimum values of f(x, y) = xy on the ellipse (x^2)/4+ y^2 = 1 (so our constraint function is g(x, y) = (x^2)/4 + y^2 ).

a) Find ∇f and ∇g.

b) You should notice that there are no places on the ellipse where ∇g = 0, so we just need to find the points on the ellipse where ∇f(x, y) = λ∇g(x, y) for some λ. Find the points on the ellipse where fx(x, y) = λgx(x, y) and fy(x, y) = λgy(x, y) for some λ. Often a good strategy to use is to solve for λ in one of the components, and then plug this in for λ in the other component (this eliminates the λ’s and allows us to solve for just x and y). Don’t forget that we want the x and y points where (x^2) /4 + y^2 = 1.

c) Plug the points from the previous step into f(x, y) to find the maximum and minimum (you should have four total points, two of these will be the maximum and two will be the minimum).

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find the maximum and minimum values of f(x,y)=xy on the ellipse 2x2+y2=4.
Find the maximum and minimum values of f(x,y)=xy on the ellipse 2x2+y2=4.
Find the maximum and minimum values of f(x,y)= xy on the ellipse 9x^2+y^2 = 8.
Find the maximum and minimum values of f(x,y)= xy on the ellipse 9x^2+y^2 = 8.
Use the Lagrange Multipliers method to find the maximum and minimum values of f(x,y) = xy...
Use the Lagrange Multipliers method to find the maximum and minimum values of f(x,y) = xy + xz subject to the constraint x2 +y2 + z2 = 4.
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=xy subject to the constraint...
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=xy subject to the constraint 25x^2+y^2=200 if such values exist. Enter the exact answers. Which is global maximum/global minimum? Enter NA in the appropriate answer area if these do not apply.
Find the absolute maximum and minimum values of the function f (x, y) = x^2 xy+on...
Find the absolute maximum and minimum values of the function f (x, y) = x^2 xy+on the region R bounded by the graphs of y = x^2 and y = x+ 2
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=6x+y on the ellipse x2+16y2=1
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=6x+y on the ellipse x2+16y2=1
Find the indicated maximum or minimum value of f subject to the given constraint. ​Minimum: ​f(x,y)=2...
Find the indicated maximum or minimum value of f subject to the given constraint. ​Minimum: ​f(x,y)=2 x^2 + y ^2 + 2 xy + 3 x + 2 y​ ;  y^2 = x + 1 The minimum value is -------------. (Type an integer or a simplified​ fraction.)
The graph of the tilted ellipse is x^2 - xy + y^2 - x - y...
The graph of the tilted ellipse is x^2 - xy + y^2 - x - y = 2 a) Find the points on the ellipse where the tangent line is horizontal b) Find the points on the ellipse where the tangent line is vertical c) What are the dimensions of the box containing the ellipse? d) What are the coordinates of the four corners of the box containing the ellipse?
Find the global maximum and global minimum of f(x, y) = y^2 +xy −x^2 on the...
Find the global maximum and global minimum of f(x, y) = y^2 +xy −x^2 on the square domain 0 ≤ x ≤ 2, 0 ≤ y ≤ 2.
Find the absolute maximum and minimum values of f(x, y) = 4xy + x^2 on the...
Find the absolute maximum and minimum values of f(x, y) = 4xy + x^2 on the triangular region D in the xy-plane with vertices (4, 0), (0, 3), and (2, 4).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT