calc notes lecture 19

calc notes lecture 19 - Second Derivative x-intercept...

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Lecture Section Objectives Assignment 18-19 3.7 Summary of Curve Sketching 3.7: 1, 5, 7, 9, 13, 19, 33, 37, 43-51 odd Understanding Goals: 1. To be able to analyze the graph of functions using previous knowledge of function. 2. To be able to recognize the graphs of simple polynomial functions. So far, we have studied several concepts that are useful in analyzing the graph of a function. x -intercept and y -intercept: set y=0, solve for x (a,0); set x=0, solve for y (0,b) Symmetry: f(-x) = f(x) symmetry with respect to the y axis; f(-x) = -f(x) symmetry with respect to x-axis Domain and range: Continuity: Vertical asymptotes: Differentiability: Relative extrema: Concavity: Points of inflection: Horizontal asymptotes: 1
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Example 1 : Analyze and sketch the graph of 2 2 2( 9) ( ) 4 x f x x . First Derivative
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Unformatted text preview: Second Derivative x-intercept y-intercept Vertical asymptotes Horizontal asymptotes Critical number Possible points of inflection Domain Symmetry Test intervals Interval f ( x ) f' ( x ) f "( x ) Characteristic of Graph 2 3 Example 2 : Analyze and sketch the graph of 2 2 5 5 ( ) 2 x x f x x . First Derivative Second Derivative x-intercept y-intercept Vertical asymptotes Horizontal asymptotes End behavior Critical number Possible points of inflection Domain Test intervals Interval f ( x ) f' ( x ) f "( x ) Characteristic of Graph 4 Example 3 : Analyze and sketch the graph of 3 2 ( ) 3 9 5 f x x x x . 5 Example 4 : Analyze and sketch the graph of 5 4 3 3 ( ) 2 5 f x x x . 6 Summary of Simple Polynomial Graphs 7 8...
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calc notes lecture 19 - Second Derivative x-intercept...

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