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184GRP2 - Math 184 Group Work 2 Instructions Please work on...

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Math 184 Group Work 2 Instructions: Please work on the following problems with your group. (This might just be the people sitting near you in class.) These problems are meant to be a bit difficult, so please spend AT LEAST 15 minutes thinking about the assignment amongst your group before coming to ask me for help. There is a page of hints at the end of the assignment; if you have thought about a problem for AT LEAST 5 minutes and don’t see how to do it, then take a look at the hints. 1. Find the derivatives of the following functions, using whatever rules you like. Remember that d dx ( e x ) = e x , d dx (ln x ) = 1 x , d dx (sin x ) = cos x , and d dx (cos x ) = - sin x . a. f ( x ) = cos( e x ) b. h ( t ) = 2 3 + 1 3 t 3 + 2 t 2 3 c. m ( x ) = sin(cos( π 2 )) d. k ( x ) = (( x 2 + 1) 3 + 2) 4 e. q ( z ) = sin( z 2 + 1) cos( z 2 + 1) ln( z 2 + 1) 1
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2. Suppose that you operate a lemonade stand, and that f ( x ) represents the revenue in dollars which you will make in a day if you purchase x lemons at the beginning of that day. a. Explain in words what the equation f (200) = 50 means. b. What sign do you think that f ( x ) will always have for this problem? Why?
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