MA 16500 Midterm: Fall 2002, 2
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/100: write your name, student id number, recitation instructor"s name and recitation time in the space provided above. Correct answers with inconsistent work may not be given credit: credit for each problem is given in parentheses in the left hand margin, no books, notes or calculators may be used on this exam. (16) 1. It is not necessary to simplify. (a) y = 3 1 + x3 (b) f (x) = tan 1(cos2 x) (c) y = x ln x (d) f (x) = sin 1 e3x. Find all points (x, y), with 0 x 2 , on the graph of the function f (x) = 2 sin x + sin2 x at which the tangent line is horizontal. (x, y) = (9) 3. = x2 + 1, nd dy dx by implicit di erentiation. (9) 4. Find the second derivative of the function y = 1 + x3. Find the derivative of the function y = x1/x. (14) 7.
