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Unformatted text preview: [ a, b ] 1. Find critical points (C.P.) – i.e. where f ( x ) = 0 or f ( x ) is undeﬁned. 2. Evaluate f at each C.P. and at the endpoints of the interval (i.e. the boundary). Largest value = Absolute Maximum Smallest value = Absolute Minimum In R 3 : How to ﬁnd Absolute Extrema 1. 2. 3. 4. 6 Example 1 Find the absolute extrema of f ( x, y ) = x 4 + y 3 +32 x9 y over the rectangular plate2 ≤ x ≤ 0,2 ≤ y ≤ 0. 7 Example 2 Same function as Example 1, f ( x, y ) = x 4 + y 3 + 32 x9 y over the region bounded by x = 2, y = 0, and y = 2 x . 8 Example 3 Find the extreme values of f ( x, y ) = xy on the unit disk, x 2 + y 2 ≤ 1. 9...
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 Spring '03
 MECothren
 Critical Point, Derivative, Multivariable Calculus, absolute extrema

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