T3ReviewAns - (a Determine the intervals where f x is...

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1205 Review Problems Test 3 Answers 1.(a) L ( x ) = 1 4 x + 7 4 (b) L (0.9) = 1.975 2. L ( x ) = 3 x ! 2 3. L ( x ) = 1 12 x ! 4 3 4. dy = (2 x + 2) dx = 4 5. dy = ! 1 2 1 ! x ( ) ! 1 2 dx = ! .01 6. Absolute Maximum at (0,5) endpoint Absolute Minimum at (2, ! 7) critical point 7. Absolute Maximum at (2,5) endpoint Absolute Minimum at (1,3) critical point 8. f ( x ) cont on [0,2] critical points: x = ± 1 (0,0) abs min 1, 1 2 ! " # $ % & abs max 9. P 3 ( x ) = ( x ! 1) ! 1 2 ( x ! 1) 2 + 1 3 ( x ! 1) 3 10. dr ! 1.99 ! 2 inches 11. f ( x ) cont on [0,4] and diff on (0,4) f (0) = f (4) = 1 c = 2 12. . one possibility: 13. a. Vertical Asymptote at x = ± 1 Horizontal Asymptote at y = ! 1 b. f ( x ) increasing (0,1) and (1, ! ) f ( x ) decreasing ( "! , " 1) and ( " 1,0) c. x = 0 local min
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d. f ( x ) cc up ( ! 1,1) f ( x ) cc down ( !" , ! 1) and (1, " ) No points of inflection e. graph: 14. (a) Determine the intervals where
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Unformatted text preview: (a) Determine the intervals where f ( x ) is increasing ___ [ ! 4, ! 1] and [3,5] ____ and the intervals where f ( x ) is decreasing _____ [ ! 1,3] ____ (b) List the x-values of the critical points of f ( x ) ___ x = ! 1, 1, 3 ___ (c) Find the local maximums of f ( x ) ____ x = ! 1 _____ and the local minimums of f ( x ) _______ x = 3 _____ (d) Determine the intervals where the graph of f ( x ) is concave up ___ (0,1) and (2,5) __ and the intervals where the graph of f ( x ) is concave down __ ( ! 4,0) and (1,2) ___ (f) Find all of x coordinates of the points of inflection ___ x = 0, 1, 2 ____...
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