CWA CH 5 FINAL_97_14 - Chapter 5 GRAPHS AND THE DERIVATIVE...

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Unformatted text preview: Chapter 5 GRAPHS AND THE DERIVATIVE 5.1 Increasing and Decreasing Functions 1. By reading the graph, f is (a) increasing on (1 ; 1 ) and (b) decreasing on ( ¡1 ; 1) : 2. By reading the graph, f is (a) increasing on ( ¡1 ; 4) and (b) decreasing on (4 ; 1 ) : 3. By reading the graph, g is (a) increasing on ( ¡1 ; ¡ 2) and (b) decreasing on ( ¡ 2 ; 1 ) : 4. By reading the graph, g is (a) increasing on (3 ; 1 ) and (b) decreasing on ( ¡1 ; 3) : 5. By reading the graph, h is (a) increasing on ( ¡1 ; ¡ 4) and ( ¡ 2 ; 1 ) and (b) decreasing on ( ¡ 4 ; ¡ 2) : 6. By reading the graph, h is (a) increasing on (1 ; 5) and (b) decreasing on ( ¡1 ; 1) and (5 ; 1 ) : 7. By reading the graph, f is (a) increasing on ( ¡ 7 ; ¡ 4) and ( ¡ 2 ; 1 ) and (b) decreasing on ( ¡1 ; ¡ 7) and ( ¡ 4 ; ¡ 2) : 8. By reading the graph, f is (a) increasing on ( ¡ 3 ; 0) and (3 ; 1 ) and (b) decreasing on ( ¡1 ; ¡ 3) and (0 ; 3) : 9. (a) Since the graph of the function is positive for x < ¡ 1 and x > 3 , the intervals where f ( x ) is increasing are ( ¡1 ; ¡ 1) and (3 ; 1 ) : (b) Since the graph of the function is negative for ¡ 1 < x < 3 , the interval where f ( x ) is decreasing is ( ¡ 1 ; 3) . 10. (a) Since the graph of the function is positive for 3 < x < 5 ; the intervals where f ( x ) is increasing is (3 ; 5) : (b) Since the graph of the function is negative for x < 3 and x > 5 , the interval where f ( x ) is decreasing are ( ¡1 ; 3) and (5 ; 1 ) . 11. (a) Since the graph of the function is positive for x < ¡ 8 ; ¡ 6 < x < ¡ 2 : 5 and x > ¡ 1 : 5 ; the intervals where f ( x ) is increasing are ( ¡1 ; ¡ 8) ; ( ¡ 6 ; ¡ 2 : 5) ; and ( ¡ 1 : 5 ; 1 ) : (b) Since the graph of the function is negative for ¡ 8 < x < ¡ 6 and ¡ 2 : 5 < x < ¡ 1 : 5 , the in- tervals where f ( x ) is decreasing are ( ¡ 8 ; ¡ 6) and ( ¡ 2 : 5 ; ¡ 1 : 5) : 12. (a) Since the graph of the function is positive for x < ¡ 3 ; ¡ 3 < x < 3 , and x > 3 , the intervals where f ( x ) is increasing are ( ¡1 ; ¡ 3) ; ( ¡ 3 ; 3) , and (3 ; 1 ) : (b) Since the graph of the function is never negative, there are no intervals where f ( x ) is decreasing. 13. y = 2 : 3 + 3 : 4 x ¡ 1 : 2 x 2 (a) y = 3 : 4 ¡ 2 : 4 x y is zero when 3 : 4 ¡ 2 : 4 x = 0 x = 3 : 4 2 : 4 = 17 12 and there are no values of x where y does not exist, so the only critical number is x = 17 12 : 297 298 Chapter 5 GRAPHS AND THE DERIVATIVE Test a point in each interval. When x = 0 ;y = 3 : 4 ¡ 2 : 4(0) = 3 : 4 > : When x = 2 ;y = 3 : 4 ¡ 2 : 4(2) = ¡ 1 : 4 < : (b) The function is increasing on ¡ ¡1 ; 17 12 ¢ : (c) The function is decreasing on ¡ 17 12 ; 1 ¢ : 14. y = 1 : 1 ¡ : 3 x ¡ : 3 x 2 (a) y = ¡ : 3 ¡ : 6 x y is zero when ¡ : 3 ¡ : 6 x = 0 x = ¡ : 3 : 6 = ¡ 1 2 and there are no values of x where y does not exist, so the only critical number is x = ¡ 1 2 : Test a point in each interval....
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This note was uploaded on 10/07/2010 for the course CALC 2302 taught by Professor Yuly during the Fall '08 term at University of Texas at Dallas, Richardson.

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CWA CH 5 FINAL_97_14 - Chapter 5 GRAPHS AND THE DERIVATIVE...

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