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0607a.monotone.extrema - MAC 2233/001-006 Business Calculus...

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MAC 2233/001-006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Name: Two points . Professor : Stephen Suen Section: Peer Leaders : Hana Aboul-Hosn, Toni Jung, Renan Mendonca 6. Increasing and decreasing properties of functions . A differentiable function f is increasing on an interval ( a,b ) if f ( x ) > 0 on the interval. It is decreasing if f ( x ) < 0 on the interval. Example . (Increasing and decreasing revenue) Recall that the monthly revenue R (in thousands of dollars) of a bakery store t months can be modelled by R ( t ) = 1 12 t 3 t 2 + 15 4 t, 0 t 8 . We shall find the intervals on which R is increasing or R is decreasing by following the following steps. (a) Find the derivative R ( t ). Solution. Using basic differentiation rules, we have R ( t ) = 1 4 t 2 2 t + 15 4 . (b) Find values (if any) of t when R ( t ) = 0. Solution. We set R ( t ) = 0 and solve for t : 1 4 t 2 2 t + 15 4 = 0 , or t 2 8 t + 15 = 0 , and after factoring ( t 3)( t 5) = 0 .
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