GW3a -

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Unformatted text preview: Mock Gateway III (Graphs) 1. f (x) = 60x3 - 30x 60x3 - 30x = 0 30x(2x2 - 1) = 0 1 x = 0, 2 1 1 Critical points: -1, - 2 , 0, 2 , 2 f (-1) = 31 1 109 f (- ) = = 27.25 4 2 f (0) = 31 1 109 f( ) = 4 2 f (2) = 211 Absolute Max: 211 Absolute Min: 109 4 2. f (x) = 2x - 3x-2 2x - 3x-2 = 0 3 2x = 2 x 3 x3 = 2 3 3 x= 2 Critical point: 3 3 2 f (x) = 2 + 6x-3 f 3 3 2 =2+6 >0 3 3 2 We have a local minimum at 3 3 . 2 Note: If a function doesn't have a local maximum or minimum, a good answer to the question of "why" is either: (a) The function is always increasing. (b) The function is always decreasing. 3. (a) 1 (b) (-, -1) (1, ) (c) (-1, 1) (d) 1 4. 4y 3 2 .... ........ .. ...... ... .... ... ... .... ... .... .... ... ... ..... ...... ... ........ ... ......... . . ............... .............. .. .. . . ... .. .. .. . . .. .. .. .. ................ ............... . . ........ ........ .. .. ..... ..... ... .... .... ... . ... ... ... ... .. .. ... .. ......... .......... .. . ... . ..... .. .. 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 1 2 3 4 x 5 5. . . . .... . . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............... . . .................. . .. . ... . .. ... . .. ... . . ... .. .. . . .. . .. .. .. . .. .. . .. . .. . .. . . .. . .. . . .. . . .. . .. . .. . . .. . . . . .. . . .. . . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................ .. ................. . . . . . ..... . . . . .... . . .. . . .. . . ... . .. . . . .. ... . . . . . . . . . . . . . . . . .. ..... . . . .. ... .. . . . . . . . . . . .. .. . .. .. . . . . .. . .. . . . . .. .. . . . .. . . . . . . . .. .. . . .. . .. .. .. . . . . . . . .. . ... . . ... .. . . . . . . . . .. . . ... . ... ..... . . . . . . . . . . . . ... . . ... . .... . ...... . . . . . .............. . . ............ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y 3 2 1 -3 -2 -1 1 2 3 .. .. . x .. -1P -2 -3 Note: The derivative of a parabola is a line, not the other way around. So for this problem, the parabola will always be your f and the line your f . Point P Q 6. R S T y + 0 0 + y 0 + + ...
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This note was uploaded on 05/15/2008 for the course MATH 231 taught by Professor Mooney during the Spring '08 term at Wisconsin Milwaukee.

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