final - APPM 2350 FINAL EXAM FALL 2007 INSTRUCTIONS...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
APPM 2350 FINAL EXAM FALL 2007 INSTRUCTIONS: Electronic devices, books, and crib sheets are not permitted. Write your (1) name, (2) instructor’s name, and (3) recitation number on the front of your bluebook. Work all problems. Show your work clearly. Note that a correct answer with incorrect or no supporting work may receive no credit, while an incorrect answer with relevant work may receive partial credit. 1. (30 Points) Find the absolute maximum and minimum values of the function f ( x, y ) = 20 - 16 x - 4 y + 4 x 2 + y 2 on the closed region bounded by the lines x = 4, y = x , and y = 0. Be sure to clearly give both the locations and values of the absolute extremum. 2. (30 points) Consider the curve y = x for 0 x 3. Find the point on the curve closest to, and furthest from, the point (2 , 0). Although this problem can be worked using simple Calculus I principles, you need to work this problem using Calculus III principles! Clearly explain your approach as you work through the problem! (Hint: you may find it useful to graph the constraint curve in the x - y plane as well as the level curves of the objective function.) 3. (30 Points) Consider a particle moving along a path in space through a temperature field T ( x, y, z ). At a particular instant in time (and only at that instant in time) the position of the particle is r = 2 i + j + k , its velocity is v = 2 i + 2 j + k , and its acceleration is a = 2 j . At the location (2 , 1 , 1) the value of the temperature is T (2 , 1 , 1) = 5 and the gradient of the temperature field at the same location is T (2 , 1 , 1) = 3 i + 2 j + k .
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern