Pre-Calc Homework Solutions 82

Pre-Calc Homework Solutions 82 - 82 Section 3.4 32x f(3 9...

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9. Note that f 9 ( x ) 5 2 32 x 1 160. lim h 0 } f (3 1 h h ) 2 f (3) } 5 f 9 (3) 5 2 32(3) 1 160 5 64 For graphical support, use the graph shown in the solution to Exercise 7 and observe that NDER ( f ( x ), 3) < 64. 10. f 9 ( x ) 5 2 32 x 1 160 f 0 ( x ) 5 2 32 At x 5 7 (and, in fact, at any other of x ), } d dx 2 y 2 } 5 2 32. Graphical support: the graph of NDER(NDER f ( x )) is shown. [ 2 1, 9] by [ 2 40, 10] Section 3.4 Exercises 1. Since V 5 s 3 , the instantaneous rate of change is } d d V s } 5 3 s 2 . 2. (a) Displacement = s (5) 2 s (0) 5 12 2 2 5 10 m (b) Average velocity 5 } 1 5 0 se m c } 5 2 m/sec (c) Velocity 5 s 9 ( t ) 5 2 t 2 3 At t 5 4, velocity 5 s 9 (4) 5 2(4) 2 3 5 5 m/sec (d) Acceleration 5 s 0 ( t ) 5 2 m/sec 2 (e) The particle changes direction when s 9 ( t ) 5 2 t 2 3 5 0, so t 5 } 3 2 } sec. (f) Since the acceleration is always positive, the position s is at a minimum when the particle changes direction, at t 5 } 3 2 } sec. Its position at this time is s 1 } 3 2 } 2 5 2 } 1 4 } m. 3. (a) Velocity: v ( t ) 5 } d d s t } 5 } d d t } (24 t 2 0.8 t 2 ) 5 24 2 1.6 t m/sec Acceleration: a ( t ) 5 } d d v t } 5 } d d t } (24 2 1.6 t ) 5 2 1.6 m/sec 2 (b)
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