MATH 19 Midterm: MATH 19 Exam 2 Winter 2012 2
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Unless otherwise stated, you may use any results from class or from sections 1. 1 - 3. 4 of the book that you like. If you use a result, be sure to verify the hypotheses are satis ed. (2) this is a closed-book exam. Prove that there is an x greater than 1 and smaller than 2 such that sin(x) = x2. Let f : r r be given by f (x) = x3 (1) find the values of x with f (x) > 0. Find the values of x with f (x) < 0. (2) find the values of x for which f is increasing. Find the values of x for which f is. 3x + 2. decreasing. (3) find the values of x for which f is concave up. Find the values of x for which f is concave down. 1 x+h h lim h 0 (2) (3)
