MATH 100 Midterm: MATH 100 KSU S13Exam3.sol

• School: Kansas State University
• Department: Mathematics
• Course: MATH 100
• Professor: All

Document Summary

Answers which are illeg- ible for the grader cannot be given credit: show your work. Except for problems 1-2, we need to see details of your computation: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 90 minutes time to complete your work. Problem 1) true/false questions (20 points), no justi cations needed. Every function f (x, y) of two variables has either a global minimum or a global maximum. Take for example f (x, y) = x + y. This function has a constant nonzero gradient and so no critical point. The linearization of the function f (x, y) = ex+3y at (0, 0) is l(x, y) = 1 + x + 3y. The gradient of f is f = hex+3y, 3ex+3yi. We have f (0, 0) = 1 so that l(x, y) = 1 + x + 3y.