APPM 1345 Midterm: appm134spring2013exam1_sol
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On what intervals is y (f) find the in ection points of y, if any. (g) sketch a graph of y. Clearly label any intercepts, local extrema, and in ection points. Solution: (a) the function is de ned when 6 x 0 or x 6 . The domain is ( , 6] . x < 6 concave down on ( , 6) The function is concave down throughout the domain. (f) there are no in ection points . (g) y x. The intercepts are therefore (0, 0) and satis es g(0) = 0. (6, 0) . (c) there are critical numbers where y = 0 at x = 4 and y is unde- 4 < x < 6 y y increasing on ( , 4) decreasing on (4, 6) (d) based on the rst derivative test, there is a local maximum value at x = 4, y = 4 2 .
