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Pre-Calc Homework Solutions 126

# Pre-Calc Homework Solutions 126 - 126 Chapter 3 Review 200...

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74. continued (c) One possible answer: If the current ridership is less than 40, then the proposed plan may be good. If the current ridership is greater than or equal to 40, then the plan is not a good idea. Look at the graph of y 5 r ( x ). [0, 60] by [ 2 50, 200] 75. (a) Since x 5 tan u , we have } d d x t } 5 (sec 2 u ) } d d u t } 5 2 0.6 sec 2 u . At point A , we have u 5 0 and } d d x t } 5 2 0.6 sec 2 0 5 2 0.6 km/sec. (b) 0.6 } r s a e d c } ? } 1 r 2 ev p o r lu ad tion } ? } 6 1 0 m s i e n c } = } 1 p 8 } revolutions per minute or approximately 5.73 revolutions per minute. 76. Let f ( x ) 5 sin ( x 2 sin x ). Then f 9 ( x ) 5 cos ( x 2 sin x ) } d d x } ( x 2 sin x ) 5 cos ( x 2 sin x )(1 2 cos x ). This derivative is zero when cos ( x 2 sin x ) 5 0 (which we need not solve) or when cos x 5 1,which occurs at x 5 2 k p for integers k . For each of these values, f ( x ) 5 f (2 k p ) 5 sin (2 k p 2 sin 2 k p ) 5 sin (2 k p 2 0) 5 0. Thus, f ( x ) 5 f 9 ( x ) 5 0 for x 5 2 k p , which means that the graph has a horizontal tangent at each of these values of x .
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