MATH 151 Midterm: MATH 151 TAMU Y2010 2010c Exam 3b Solutions
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Solutions-form b: d. where is f (x) = ex3. 3x increasing? f (x) is increasing where f (x) > 0. f (x) = (3x2 3)ex3. This yields critical numbers of x = 1. Now f (x) < 0 on the interval ( 1, 1) and f (x) > 0 on the intervals ( , 1) (1, ): b. The critical numbers are those numbers c in the do- main of f where f (c) = 0 or f (c) does not exist. By viewing the graph below, f ( 2) = 0. Furthermore, f ( 6) and f (2) do not exist. Thus the critical num- bers are x = 2, x = 6 and x = 2: b. Recall that the domain of arccos x is the range of cos x = [ 1, 1]. Thus the domain of arccos(3 + t) is all t such that.
