13'8 Maxima, Minima, and Saddle Points

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13.8 Maxima, Minima, and Saddle Points
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Critical Points

• Let zf(x,y). and f is continuous at (a,b).
• The point (a,b) is a critical point off if
• fx(a,b)fy(a,b)0 or fx or fy fails to exist.

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Second Derivative Test

• Assume the first and second derivatives of f are
  continuous throughout an open region containing
  (a,b), a critical number of f.
• Let D be the derterminant

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Extreme Value Theorem

• If f is continuous on the closed interval a,b,
  then f takes on both an absolute maximum and
  absolute minimum values on a,b.

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Extreme Value Theorem

• If f is continuous on a closed region R, then f
  takes on both an absolute maximum and absolute
  minimum values on this closed region.