MATH 100 Midterm: MATH 100 KSU SolutionsExam3SCASpring2012

• 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. Mark for each of the 20 questions the correct letter. F f (x, y) and g(x, y) = f (x2, y2) have the same critical points. The function g has always (0, 0) as a critical point, even if f has not. If a function f (x, y) = ax + by has a critical point, then f (x, y) = 0 for all (x, y). At a critical point the gradient is (a, b) = (0, 0), which implies f = 0. Given 2 arbitrary points in the plane, there is a function f (x, y) which has these points as critical points and no other critical points.