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Practice Quiz 3d

Practice Quiz 3d - (d Find all local maximum values for...

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Practice Test IIID for Math 1501, Calculus I I A disk of paper is to be formed into a conical cup as follows: A wedge is cut out and removed along two radii. The two edges thus formed are then joined without overlap. Let x be the fraction of the disk that is removed. What should x be for the volume of the cup to be maximized, and what is the maximal volume? (Recall that the volume of a right cylindrical cone with radius r and height h is π 3 r 2 h .) II Let f be the function f ( x )= x 2 - x 1 - x 2 . Answer the following questions, and justify your answers. (a) Find all asymptotes of this function, if any. (b) Find values of x for which f 0 ( x ) = 0, that is, all critical numbers ,i fany .
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Unformatted text preview: (d) Find all local maximum values for this function, if any. III Answer the following questions using the Mean Value Thoerem. Let f be a function that satisﬁes: f (1) = 1 f (4) = 2 and | f ( x ) | ≤ 2 for all 1 ≤ x ≤ 4 . (a) Could it be true that f (2) = 0? (b) Could it be true that f (2) =-1? (c) Could it be true that f (2) =-2? (d) Could it be true that f (2) = 5? (e) Could it be true that f (3) = 5? (f) Could it be true that f (3) = 0? IV Let F be a function such that F 00 ( x ) = x-x 2 for all x . Suppose also that F (0) = 0 and F (1) = 1. ﬁnd a formula for F ( x )....
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