Labelling - Calculus - Solved Exam, Exams of Calculus

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—_ MATH 105 Final Exam Review II December 14, 2004 1.) Consider the function f(x) = 2° — 2x3 on the interval [-2,2]. a) Find the 2-coordinate(s) of any and all roots of f. These are the solutions of f(x) = 0. (No need for calculus yet, but this will help us sketch f later.) O= x*-2,? O= ¥>(x3-2) K=O, K= 2 | Es b) Find the z- and y-coordinates of any and all local extrema and classify each as a local maximum or local minimum. £(r)2 -ex” 1f WON 4 local max? Rone 0268 LH TT Tt local mm (1-1) X>o0, XS X20 3 Y¥=0 x=) 3 grcl c) Find the z- and y-coordinates of any and all global extrema and classify each as a global maximum or global minimum. From number Ine tr Cb), seo trek [9 lobe mm is (U-) Global max ts at an evel pt £¢2)= 60 £(2) = 46 S, global Max Ts (-2,8) . d) Find the x-coordinate(s) of any and all inflection points. f(x) = 3Ox4 - 12x Core Cone CC ue O= Gx(Sx>—2) | for, deen, oh u 3 K=O, KF 5 As € ° 3 ec) Sketch f(z), labelling all the points you found above. (26) &