lecture23 - a,b ). 3) Find the absolute extrema of f on (...

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Lecture 23 1 Lecture 23, (Sec. 4.4) Absolute Extrema ex. Find all relative extrema of f ( x ) = x 2 - x 4 2 .
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Lecture 23 2 Sketch the graph of f ( x ) = x 2 - x 4 2 .
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Lecture 23 3 Given a function f and an x -value c in the domain of f . The function value f ( c ) is the absolute maximum value of f if for each x in the domain of f , The function value f ( c ) is the absolute minimum value of f if for each x in the domain of f ,
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Lecture 23 4 Absolute Extrema on an Interval: How to find it? If f is continuous on an open interval I and c is the only critical value on the interval: 1) 2)
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Lecture 23 5 ex. Find the absolute extrema of f ( x ) = x 2 + 18 x - 3 on (0 , ).
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Lecture 23 6 Absolute Extrema on a Closed Interval 1) Find the critical points of f on the interval [ a,b ]. 2) Find the relative extrema of f on (
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Unformatted text preview: a,b ). 3) Find the absolute extrema of f on ( a,b ). Lecture 23 7 4) Find the absolute extrema of f on [ a,b ]. Theorem Lecture 23 8 To nd absolute extrema of function f on [ a,b ]: 1) Is f continuous on [ a,b ]? 2) 3) NOTE: Lecture 23 9 ex. Find the absolute extrema of f ( x ) = x 3-3 x 2 + 2 on [-1 , 1]. Lecture 23 10 ex. Find the relative extrema of f ( x ) = x 3-3 x 2 + 2. Lecture 23 11 ex. Find the absolute extrema of f ( x ) = x 2 + 18 x-3 on [2 , 12]. Lecture 23 12 ex. a) Find the absolute extrema of f ( x ) = x 2 + 18 x-3 on [-1 , 12]. b) Find the absolute extrema of f on (0 , 12]....
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lecture23 - a,b ). 3) Find the absolute extrema of f on (...

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