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lecture26hout - MATH 006 Calculus and Linear...

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MATH 006 Calculus and Linear Algebra (Lecture 26) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 11
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Outline 1 General Patterns for Analyzing Graphs 2 Graphing a Polynomial Function 3 Application: Point of Diminishing Returns Albert Ku (HKUST) MATH 006 2 / 11
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General Patterns for Analyzing Graphs General Patterns for Analyzing Graphs Albert Ku (HKUST) MATH 006 3 / 11
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Graphing a Polynomial Function Graphing a Polynomial Function Suppose y = f ( x ) where f ( x ) is a polynomial function. The following is the procedure for graphing y = f ( x ): 1 Analyze f ( x ) : Find the x -intercept(s) and y -intercept of f ( x ). 2 Analyze f ( x ) : Find the critical point(s) of f ( x ). Construct a sign chart for f ( x ) and determine the interval(s) where f ( x ) is increasing and decreasing. Find local maxima and minima (if any). 3 Analyze f ( x ) : Construct a sign chart for f ( x ), determine the interval(s) where f ( x ) is concave upward and concave downward. Find the inflection point(s) of f ( x ) (if any).
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