APPM 1345 Midterm: appm134spring2014exam1_sol
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Justify your answer using appropriate limits. (d) the rst derivative is y = x2 + 4x + 5 (x + 2)2. On what intervals is y increasing? decreasing? (e) find the local maximum and minimum values of y, if any. (f) the second derivative is y = 2 (x + 2)3 . On what intervals is y concave up? concave down? (g) find the in ection points of y, if any. (h) sketch a graph of y. Clearly label any intercepts, asymptotes, local extrema, and in ection points. Solution: (a) the domain is ( , 2) ( 2, ) . (b) if x = 0 then y = 5/2. If y = 0 then x = (c) there is a vertical asymptote at x = 2 where the denominator equals 0: The intercepts are (0, 5/2), ( 5, 0), ( . 5, 0) . lim x 2+ x2 5 x + 2.
