(From The Hollow Men, by T. S. Eliot.)
Ah, me. Nobody got even a single point of the eight I allotted to Problem 11c. I ended up treating 11c as extra credit, leaving a nice round 200 non-extra-credit points. However, I was not very happy with what I saw on any part of Problem 11, since in class I went through exactly the steps in parts (a), (b) and (c) to show you that a function can have all its directional derivatives exist at a point, yet not be differentiable at that point. The example I used of a function with this property was exactly the function in parts (b) and (c) of the exam problem. But, even after taking part (c) out of the denominator, the class average on problem 11 was only 14% (about two out of the 14 non-EC points), with only one student getting more than four points.
Moral: if you don't understand everything in your notes, you should not be satisfied with your studying.
167,
157,155,
146,
.
124,122,
114,110,
104,101,100,
97,
87,
78,
66, 65
167
157
A's 155
---------------
A-'s, B+'s, & B's 146
---------------
B-'s, C+'s, & C's 124
122
114
110
104
101
100
97
87
B-'s, C+'s, & C's 78
---------------
C-'s, D+'s, & D's 66
65