Wetzel

Math 140

3.6 – A Summary of Curve Sketching

Steps:

            1.)  1^st Derivative Sign Diagram

·        Critical Numbers

·        Extrema

·        Increasing / Decreasing Intervals

            2.)  2^nd Derivative Sign Diagram

·        Points of Inflection

·        Concavity Intervals

            3.)  Asymptotes

·        Vertical and Removable Discontinuities

·        Horizontal

·        Oblique

            4.)  Intercepts

·        X intercepts

·        Y intercepts

Ex.: 

1.)                    2.)                     3.) 

4.)  The profit P (in dollars) made by a fast-food restaurant selling x hamburgers is

                      0 < x < 35,000

      Find the open intervals on which P is increasing.

HW:  p.215  #1-4all, 1, 9, 11, 15, 17, 19