APPM 1350 Midterm: appm1350spring2015exam2_sol
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Make sure to verify the points are indeed points of in ection. Critical points are where the derivative is equal to zero, or is unde ned. f (x) = 2 cos x sin x. This derivative is de ned for all x values. However it equals zero at several x values within the interval of concern. f (x) = 0 x = , . Now we check the behavior of the function between the critical points. f ( 3 f ( . Therefore f (x) is decreasing on [ , f (x) is increasing on [ . 2 , (b) possible locations of points of in ection are found where the second derivative equals zero, or is unde ned. f (x) = 2(cos2 x sin2 x) = 2 cos 2x. These locations are only possible x value locations of points of in ection.
