sec43supp - Math M119 Section 4.3 Supplement Local...

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Math M119 Section 4.3 Supplement Local (Relative) Max and Local Min: where f ’ ( x ) = 0 and f ” ( x ) < 0 for local max (slope of tangent line = 0, concave down) f ’ ( x ) = 0 and f ” ( x ) > 0 for local min (slope of tangent line = 0, concave up) f’ ( x ) does not exist but f ( x ) does Global Max and Global Min: The absolute highest and lowest points of the function including the end points. a) Open Interval, No End Points (entire real line): Local Maximum at: q Local Minimum at: p and r No Global ( Absolute ) Maximum Global ( Absolute ) Minimum at: p Local Maximum at: p and r Local Minimum at: q Global ( Absolute ) Maximum at: p No Global ( Absolute ) Minimum b) Closed Interval, With End Points such as a < x < b : Local Maximum at: a, q and b Local Minimum at: p and r Global ( Absolute ) Maximum at: b Global ( Absolute ) Minimum at: p Local Maximum at: p and r Local Minimum at: a , b , and q Global ( Absolute
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This note was uploaded on 02/29/2012 for the course MATH 119 taught by Professor Maanomran during the Fall '09 term at Indiana University-Purdue University Fort Wayne.

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sec43supp - Math M119 Section 4.3 Supplement Local...

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