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Unformatted text preview: f (1) = Â¡ 2, make a possible sketch of f ( x ). 6? Â± 9 We have a useful application of derivatives and the shape of a graph: Second Derivative Test Suppose that f 00 ( x ) is continuous near c . I. If f ( c ) = 0 and f 00 ( c ) then f has a local at c . II. If f ( c ) = 0 and f 00 ( c ) then f has a local at c . ex. Use the Second Derivative Test if possible to ï¬‚nd the local (relative) extrema of f ( x ) = 5 x 3 Â¡ 3 x 5 . 10 Try These! 1) Find the relative extrema and inÂ±ection points of each of the following functions. Sketch a graph of the function. a) f ( x ) = x 4 Â¡ 2 x 3 + 2 x Â¡ 1 = ( x Â¡ 1) 3 ( x + 1) b) f ( x ) = 3 x 2 = 3 + 2 x 2) Use the Second Derivative Test to ï¬‚nd the local maximum and minimum values of f ( x ) = x 4 Â¡ 4 x 3 + 4 x 2 . Conï¬‚rm by using the First Derivative Test....
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 Spring '08
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 Calculus, Geometry

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