# P22 - Project 22 MAC 2311 YOU MUST SHOW YOUR WORK TO...

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Project 22 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! 1. Examine the function g ( t ) = 50 + 30( t - 1) 1 3 e - 1 6 t . a) Calculate g 0 ( t ). b) Find the critical numbers of g ( t ). c) Do any of the critical numbers that you found in part(b) correspond to horizontal tangent lines? vertical tangent lines? Which ones? d) Find the maximum and minimum value(s) of g ( t ) on [0 , 9]. e) Use a number line to ﬁnd the intervals on which g 0 ( t ) is positive and negative. What seems to be the relationship between the sign (+ or - ) of g 0 ( t ) and the maximum value? Why might this be true (think of positive/negative slopes)? f) Suppose g ( t ) represents the temperature (in F ) of a cold storage room t hours after the room is accidently left open. What is the initial room temperature (to the nearest degree)? What is the maximum room temperature (to the nearest degree), and after how many hours does it occur?

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g) Around what instant does the room seem to experience the most rapid change in temperature? (For this particular function, the answer should
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P22 - Project 22 MAC 2311 YOU MUST SHOW YOUR WORK TO...

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