MATH 100 Midterm: MATH 100 KSU TestSolutionsExam 2&3SCASpring2012
15 Feb 2019
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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. Given a unit vector v, de ne g(x) = dvf (x). If at a critical point, for all vectors v we have dvg(x) > 0, then f is a local maximum. On every line through the critical point, we have a local minumum. So, it is a local minimum, not a local max. Assume f satis es the pde fx = fy. Use clairot"s theorem tells gx = fyx = fxy = gy. The equation = /4 in spherical coordinates ( 0, 0 , 0 .
