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MAC2233-AN3 - MAC2233 Survey of Calculus Practice Test#3 1...

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Survey of Calculus MAC2233 Practice Test #3 1) For the function graphed to the right, identify: a) The Critical Numbers------------ 0 , 2 b) Relative Extrema------------------ Rel. Max. - (0,3) Rel. Min. - (2,1) c) Points of Inflection---------------- (1,2) d) Increasing Intervals-------------- ( ,0) (2, ) ¨ ¥ e) Decreasing Intervals-------------- (0,2) f) Concave Upward Intervals------ (1, ) ¥ g) Concave Downward Intervals-- ( ,1) 2) Use the following information to graph the function f(x): f ¢ (x): - | + | - | + | + | - | - | + | + | + | 2 4 6 8 10 12 14 16 18 20 f ¢ ¢ (x): + | + | - | - | - | - | + | + | + | + | 2 4 6 8 10 12 14 16 18 20 6 lim ( ) x f x fi =-¥ x y 0 2 4 6 8 10 12 14 16 18 13 8 10 Und. 10 13 9 1 8 20
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3) For the function, 3 x 15 x 6 x f(x) 2 3 + - - = , identify: a) The Critical Numbers -------- -1 , 5 b) Relative Extrema ------------- Relative Maximum (-1,11) Relative Minimum (5,97) c) Points of Inflection ------------ (2, 43) - d) Increasing Intervals ---------- ( , 1) (5, ) -¥ - ¨ ¥ e) Decreasing Intervals --------- ( 1,5) - f) Concave Upward -------------- (2, ) ¥ g) Concave Downward ----------- ( ,2) Increasing/Decreasing Intervals Concavity Upwards/Downwards 2 f '(x) 3x 12x 15 0 3(x 1)(x 5) 0 Critical.Values;x 1;x 5 Intervals;( , 1);( 1,5);(5, ) f '( 2) 21;f'(0) 15;f'(6) 21 Increasing;Decreasing:Increasing f( 1) 11;f(5) 97 rel.max( 1,11);rel.min(5, 97) = - - = + - = = - = -¥ - - ¥ - = = - = - = = - - - f ''(x) 6x 12 0 x 2 Intervals;( ,2);(2, ) f ''(0)
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