MA 123 , Previous Exam 2 Answers
- 1) a) 5 \pi (sin \pi x + cos \pi x)^4 (cos \pi x - sin \pi x)
- 1) b) (-3x^2 - 6x + 38) / (x^2 - 6x + 2)^3
- 2) 2 ft. / min.
- 3) 0.8
- 4) 1 / (2y - 1)
- 5) Absolute minimum of -1/2 at x = -\pi/4
Absolute maximum of 1/2 at x = \pi/4
- 6)
- a) Increasing on (-1, 1). Decreasing on (-\infty, -1) and (1,
\infty).
Relative minimum at (-1 , -1/2). Relative maximum at (1, 1/2).
- b) Concave down on (-\infty, -\sqrt 3) and (0, \sqrt 3) .
Concave up on (-\sqrt 3, 0) and (\sqrt 3, \infty)
Inflection points: (-\sqrt 3, -(\sqrt 3)/4), (0,0) , (\sqrt 3, (\sqrt 3)/4)
- c) No vertical asymptotes. Horizontal Asymptote y = 0.
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