APPM 1350 Midterm: appm1350fall2017exam2_sol
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Fall 2017: (28 pts) the following problems are not related. (a) let y = cos4(cid:0)3u2(cid:1). Find dy/du. (b) let x y + 4 = y2 42. Find dy/dx at the point (3, 5). (c) suppose that 2 f (x) 10 for all values of x. Find the smallest and largest possible values of f (15) f (6). Find an equation for the slant asymptote of y. (it is not necessary to evaluate any limits when justifying your answer. ) Solution: (a) (6 pts) dy du y = cos4(cid:0)3u2(cid:1) = 24u cos3(cid:0)3u2(cid:1) sin(3u2) (b) (10 pts) use implicit differentiation. 2 y + 4 dy dx x xpy + 4 = y2 42. +py + 4 = 2y py + 4 = dy dx dy dx dy dx(cid:12)(cid:12)(cid:12)(cid:12)(3,5) dy dx (cid:18)2y . 19 (c) (6 pts) by the mean value theorem, f (15) f (6) = f (c)(15 6) for some c in (6, 15).
