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 isgreater than or equal to 40, then the plan is not a goodidea. Look at the graph of y5r(x).[0, 60] by [250, 200]75. (a)Since x5tan u, we have }ddxt}5(sec2u)}ddut}5 20.6 sec2u. At point A, we have u50 and }ddxt}5 20.6 sec20 5 20.6 km/sec.(b)0.6 }rsaedc}?}1 r2evporluadtion}?}610msienc}= }1p8}revolutions perminute or approximately 5.73 revolutions per minute.76.Let f(x)5sin (x2sin x). Then f9(x)5cos (x2sin x)}ddx}(x2sin x)5cos (x2sin x)(12cos x). This derivative is zero whencos (x2sin x)50 (which we need not solve) or when cos x51,which occurs at x52kpfor integers k. For eachof these values,f(x)5f(2kp) 5sin (2kp2sin 2kp)5sin (2kp20)50. Thus,f(x)5f9(x)50 for x52kp,which means that the graph has a horizontal tangent at eachof these values of x.
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