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Unformatted text preview: c,f ( c )) is neither a relative maximum nor a relative minimum. Second Derivative Test : Let ( c,f ( c )) be a critical point. (a) If f 00 ( c ) &lt; 0, then the point ( c,f ( c )) is a relative maximum. (b) If f 00 ( c ) &gt; 0, then the point ( c,f ( c )) is a relative minimum. Note that if f 00 ( c ) = 0 or if f 00 ( c ) is undened, then the test fails and the rst derivative test should be used instead. 1 2 5. Find the points of inection that are all values of x where f 00 ( x ) = 0 and f 00 changes the sign at those points. 6. Knowing the points of inection, determine where the function f ( x ) is concave up or concave down. (a) f ( x ) is concave up where f 00 ( x ) &gt; 0. (b) f ( x ) is concave down where f 00 ( x ) &lt; 0. 7. Sketch the curve using all information....
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 Spring '08
 YOUNG
 Mathematical analysis, relative maximum

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