05m2p

# 05m2p - s = t 3-6 t 2 + 15 t + 1 , where t is the time...

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3A Practice Sheet for Midterm II Spring 2005 Midterm II is on May 20. It covers 3.1-3.8, 3.10,4.1-4.3 Part I. Finding derivatives a) All derivative formulas b) Rules of derivative c) Implicite diﬀerentiation d) Logarithmic derivative e) higher derivative Part II Application of derivative a) Rate of change in science, e.g. if s(t) is distance, then s’(t) is the velocity b) Related rates c) Find absolute max, min of continuous functions on a closed interval d) Find when f is increasing, decreasing, concave up, concave down, local max. local min, inﬂection point Practice Problems: 1. Find f 0 ( x ) for each of the following (a) f ( x ) = r x + q x + x (b) f ( x ) = 3 q ln( x 6 + 1) (c) f ( x ) = x sin x d) f ( x ) = sin - 1 ( e 5 x ) e) Find f (50) ( x ) for f ( x ) = cos 2 x . 2. Find the absolute maximum and minimum values of the function f ( x ) = x x 2 +1 on the interval [0 , 2]. 3. A moving particle has its position given by the function
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Unformatted text preview: s = t 3-6 t 2 + 15 t + 1 , where t is the time after the motion starts and measured in seconds, and s in feet. a). When is the particle at rest? b). When is the particle moving forward? c). Find the total distance traveled during the rst 6 seconds. 4. Find y if x sin y = cos 2 y . 5. Given f ( x ) = x 6-12 x 2 + 3, ll in the following table. increasing on . decreasing on . concave up on . concave down on . local maximum at . local minimum at . inection point . 6. Two cars start from the same point. One travels east at 60 miles per hour and the other travels north at 45 miles per hour. At what rate is the distance between them changing 2 hours later?...
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