MATH 21A Midterm: MATH 21A Harvard 21a Fall 16Practice5
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Tth 11:30 jameel al-aidroos: 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. Except for problems 1-3, we need to see details of your computation: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 180 minutes time to complete your work. The tangent plane of the surface z = f (x, y) at a local maximum of f is parallel to the xy-plane. For any smooth functions f (x, y), x(t), y(t), we have d fx(x(t), y(t))x (t) + fy(x(t), y(t))y (t). At a local maximum of a function f (x, y) we always have fxx 0 and fyy 0.
