2311_MG3_DefDeriv_2.1,2.7,2.8_F11 - MAC2311 MG3 (2.1, 2.7,...

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MAC2311 MG3 (2.1, 2.7, 2.8) Name: _____________________________________ Fall 2011 Section: (circle yours) MWF 9:00 MWF 10:00 Directions : Use all available resources, including the math lab, Teague’s office hours, and fellow students. To justify answers and earn partial credit, show work in the spaces provided on this document. MG3 is due at the start of class on Friday 9/23/11 . Late papers will be penalized on a case-by-case basis, but typically a one letter grade (10%) penalty per day. Derive 6 Remarks : Once an expression in one variable [like t or x ] has been authored, it can be assigned function notation as follows. Right-click the expression , Copy , click the Author menu , choose Function Definition , type the desired function notation [like s(t) or f(x) ] in the Function Name and Arguments field, right-click in the Function Definition field, and paste the expression there. When you click OK the function notation and expression appear with the := symbol instead of a regular = symbol. From this point forward in your Derive session, the software be able to simply or evaluate function notation expressions that you author, like f(2) or f(2+h). Also be aware that you can get the decimal form for an exact numerical result by highlighting it and clicking the icon. Tangent Line Slopes; Instantaneous Velocity; The Derivative For a function given by ( ) y f x = , the average rate of change of f over the interval a x b is given by ( ) ( ) f b f a b a - - . Graphically, this is the slope of the line through points ( ) , ( ) a f a and ( ) , ( ) b f b . In physical terms, let ( ) s t represent the position of a moving object at time t , measured from an established origin. The object’s average velocity over the interval 1 2 t t t ≤ ≤ is given by ( ) ( ) 2 1 2 1 change in postion change in time ave s t s t v t t - = = - . Def . Consider function ( ) f x . The derivative of f at x is … i) (conceptual) … the instantaneous rate of change of f at x . ii)
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2311_MG3_DefDeriv_2.1,2.7,2.8_F11 - MAC2311 MG3 (2.1, 2.7,...

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