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# lecture28hout - MATH 006 Calculus and Linear Algebra...

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MATH 006 Calculus and Linear Algebra (Lecture 28) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 15

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Outline 1 Absolute Maxima and Minima 2 Second Derivative and Extrema Albert Ku (HKUST) MATH 006 2 / 15
Absolute Maxima and Minima Local Extrema and Absolute Extrema Deﬁnition If f ( c ) f ( x ) for all x in the domain of f , then f ( c ) is called the absolute maximum of f . If f ( c ) f ( x ) for all x in the domain of f , then f ( c ) is called the absolute minimum of f . Albert Ku (HKUST) MATH 006 3 / 15

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Absolute Maxima and Minima The following ﬁgure illustrates the diﬀerence between local and absolute maximum/minimum: Albert Ku (HKUST) MATH 006 4 / 15
Absolute Maxima and Minima Remarks A local maximum/minimum may not be an absolute maximum/minimum. If f has only one critical value and it is a local maximum/minimum, then it is also an absolute maximum/minimum. There exist a function that has no absolute maximum/minimum. Albert Ku (HKUST) MATH 006 5 / 15

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Absolute Maxima and Minima Example Find the absolute maxima and minima of the following functions
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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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lecture28hout - MATH 006 Calculus and Linear Algebra...

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