{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

final-practice2

# final-practice2 - Problem 1 Find the critical points of the...

This preview shows pages 1–3. Sign up to view the full content.

Problem 1. Find the critical points of the function f ( x, y ) = 2 x 3 - 3 x 2 y - 12 x 2 - 3 y 2 and determine their type i.e. local min/local max/saddle point. Are there any global min/max? Problem 2. Determine the global max and min of the function f ( x, y ) = x 2 - 2 x + 2 y 2 - 2 y + 2 xy over the compact region - 1 x 1 , 0 y 2 . Problem 3. Using Lagrange multipliers, optimize the function f ( x, y ) = x 2 + ( y + 1) 2 subject to the constraint 2 x 2 + ( y - 1) 2 18 . Problem 4. Consider the function w = e x 2 y where x = u v, y = 1 uv 2 . Using the chain rule, compute the derivatives ∂w ∂u , ∂w ∂v . Problem 5. (i) For what value of the parameter a , will the planes ax + 3 y - 4 z = 2 , x - ay + 2 z = 5 be perpendicular? (ii) Find a vector parallel to the line of intersection of the planes x - y + 2 z = 2 , 3 x - y + 2 z = 1 . (iii) Find the plane through the origin parallel to z = 4 x - 3 y + 8 . (iv) Find the angle between the vectors v = (1 , - 1 , 2) , w = (1 , 3 , 0) . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(v) A plane has equation z = 5 x - 2 y + 7 .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern