lecture27hout

# Lecture27hout - MATH 006 Calculus and Linear Algebra(Lecture 27 Albert Ku HKUST Mathematics Department Albert Ku(HKUST MATH 006 1/8 Outline 1

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MATH 006 Calculus and Linear Algebra (Lecture 27) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 8

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Outline 1 Graph-sketching Techniques 2 Examples Albert Ku (HKUST) MATH 006 2 / 8
Procedure for Graph-sketching Let y = f ( x ), where f ( x ) is not necessarily a polynomial function. The following is the procedure for sketching the graph of y = f ( x ): 1 Find the domain of f 2 Find the intercepts. 3 Find asymptotes (vertical/horizontal) 4 Find f 0 ( x ) and construct the sign chart for f 0 ( x ). Then locate the critical value(s), local maxima and local minima and the intervals for which the function is increasing and the function is decreasing. 5 Find f 00 ( x ) and construct the sign chart for f 00 ( x ). Then locate the inﬂection point(s), the interval for which the function is concave up and the function is concave down. 6 Sketch the graph of y = f ( x ). Albert Ku (HKUST)

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## This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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Lecture27hout - MATH 006 Calculus and Linear Algebra(Lecture 27 Albert Ku HKUST Mathematics Department Albert Ku(HKUST MATH 006 1/8 Outline 1

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