day16 - G raphing S egment C urve S ketching C hecklist...

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2. Graphing Segment Curve Sketching Checklist Note: • 'd items are the only ones which apply t6'OiYnomial function"S) I. Information from the function f (x) itself: ~. Intercep~ B. Asymptotes 1. Vertical Asymptotes: x = a is a VA if lim f(x) = ±oo . z-+a 2. Horizontal Asymptotes: y = b is a HA if lim I(x) = b. z-+±oo C. Restrictions on the domain ("holes," excluded regions, etc.) and discontinuities. II. Information from the Derivative I'(x): • A. Horizontal Tangents: x -COOl' ma es 0 pomts where tangent line is horizontal are found by solving I' (x) = 0 . B. Vertical Tangents: x -coordinates are those values x = c for which I ( c) exists, but lim I'(x) = ±oo . z-+c • C. Intervals of Increase and Decrease: 1. I (x) is increasing on an lIlt.erva if I' (x) > 0 for all x in that interval. x is decreasing on an interval if f'(x) < 0 for all x in that interval. Local Maxima and Minima (1st derivative test): oca maximum at x = c if the sign of x is as shown for x near c: sign of I'(x)
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This note was uploaded on 12/05/2011 for the course MATH 111 taught by Professor Bang during the Fall '08 term at Emory.

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day16 - G raphing S egment C urve S ketching C hecklist...

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