3_4Concavity2ndDerivTest

3_4Concavity2ndDerivTest - 3.4 Concavity & the 2nd...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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) ...
View Full Document

This note was uploaded on 09/09/2011 for the course MATH 1431 taught by Professor Any during the Fall '08 term at University of Houston.

Ask a homework question - tutors are online