MATH 230 Midterm: Test 2 spring 2013
15 Feb 2019
School
Department
Course
Professor
Northwestern University NetID:
ID #:
Math 230 Test #2
Spring Quarter 2013
Thursday, May 23, 2013
Complete the front page!!!! [2 points!]
Instructions: Show ALL of your work on the pages provided! Explain your reasoning using
complete sentences and correct grammar, spelling, and punctuation. All numerical answers MUST
be exact; e.g., you should write πinstead of 3.14...,√2 instead of 1.414..., and 1
3instead of 0.3333...
Make sure that your final answer is clearly indicated. This test has eleven pages. Check to make sure
you have pages 1 - 11. Calculators, course notes, textbooks, etc. are NOT allowed.
Do not write your name on this exam!
Write your NetID and your Student ID Number in the spaces provided at
the top of this page.
Mark your section!!
XSec. # Time Instructor
31 9:00 Belt
41 10:00 Belt
51 11:00 Lizzie
61 12:00 Goldstein
71 1:00 Garton
81 2:00 TiM
Question Possible Points Score
Front Page 2
1 10
2 14
3 12
4 8
5 10
6 12
7 14
8 18
Total 100
Math 230 Test 2 Spring Quarter 2013 Page 2 of 11
Question 1. A contour map for a function of two variables, f(x, y) is given below.
(a) (2 points) What is f(P)?
Math 230 Test 2 Spring Quarter 2013 Page 3 of 11
(b) (2 points each) Use the contour map on the previous page to determine the sign (positive,
negative, or zero) of each of the following partial derivatives of fat the point P.Circle your
answers.
(i) fx(P) is positive /zero /negative
(ii) fy(P) is positive /zero /negative
(iii) fxx(P) is positive /zero /negative
(iv) fyy(P) is positive /zero /negative
