MATH 21A Midterm: MATH 21A Harvard 21a Fall 13slides
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Tth 11:30 francesco cavazzani: start by printing your name in the above box and check your section in the box to the left, do not detach pages from this exam packet or unstaple the packet, please write neatly. Answers which are illeg- ible for the grader cannot be given credit: show 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. If a function f (x, y) = ax + by has a critical point, then f (x, y) = 0 for all (x, y). 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. If (x0, y0) is the maximum of f (x, y) on the disc x2 +y2 1 then x2.
