Unformatted text preview: 3.4 Concavity & the 2nd Derivate Test
Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Problems for 3.4 Title: Intro (1 of 13) Consider: y = x3 x Graph of function 1st Derivative: graph, slope of, relate to y? 2nd derivative: graph, relate to y? Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Problems for 3.4 Title: sketch (2 of 13) Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY
Problems for 3.4 Title: with 1st derivative (3 of 13) Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY
Problems for 3.4 Title: with 1st and 2nd derivatove (4 of 13) Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Problems for 3.4 Title: relate 2nd deriv to f (5 of 13) Similar to previous example. Even though no relative extrema, it is still c.u. when x>0 and c.d. when x<0. Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY
Problems for 3.4 Title: simple example (6 of 13) Definition of Concavity or when f '' (x) >0 or when f '' (x) <0 Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY
Problems for 3.4 Title: def: concavity (7 of 13) 2nd Derivative Test
(horizontal slope) ( C.U. ) ( C.D. ) Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Problems for 3.4 Title: 2nd deriv Test (8 of 13) Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Problems for 3.4 Title: ex: 2nd deriv>rel extr (9 of 13) Example: G: h(x) = x5 5x + 2 F: open interval where c.u. and c.d. Title: Oct 293:42 PM (10 of 13) Definititon of Point of Inflection Title: Oct 293:43 PM (11 of 13) Theorum: Points of Inflection Title: Oct 293:44 PM (12 of 13) Example: G: f(x) = 2x3 3x2 12x +5 F: IP Title: Oct 293:46 PM (13 of 13) ...
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 Derivative, Differential Calculus, Slope, Westchester Community College, Calculus Home Page

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