MATH 021 Study Guide - Midterm Guide: Inverse Function, Minimax, Maxima And Minima
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Uc merced, fall 2006: (20 points, 4 points each) determine whether the following statements are true or false. [cosh2( x) sinh2( x)] = 0. (c) (d) sin(arctan(x)) = x. 1 x2 (e) if f (x) is de ned for all x and f has a maximum at x = 1, then f (1) = 0. Answers: (a) false (b) false (c) true (d) false (e) true: (24 points: 8 points each) find the derivative of the following functions with respect to x. (a) x 6 x + 7. Solutions: (b) (1 + x2) arcsin(x) (c) tan(ln(1 x)) (a) (b) (c) d dx (cid:18) x 6 x + 7(cid:19) = (x + 7) (x 6) (x + 7)2. 13 (x + 7)2 d dx (cid:0)(1 + x2) arcsin(x)(cid:1) = 2x arcsin(x) + (1 + x2) 1 x2 d dx (tan(ln(1 x))) =
