CABChp4-3BNTsexample

CABChp4-3BNTsexample - at f(1) = − 27 intervals f(x)...

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Your problem. Name ____________________________________ Notes CalcAB Chp 4-3B Connections f(x), f '(x), and f ''(x) Example (d) Ex(d)— Follow same direction as previous two examples. f(x) = x 4 12x 3 + 48x 2 64x f '(x) = 4x 3 36x 2 + 96x 64 factoring help: f '(x) = 12(x 4) 2 (x 1) x = 4 x = 1 even multiplicity bec (x 4)(x 4) EVP at f(1) = 27 f ''(x) = 4x 3 36x 2 + 96x factoring help: f ''(x) = 12(x 4) (x 2) x = 4 x = 1 PI
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Unformatted text preview: at f(1) = − 27 intervals f(x) f'(x) f''(x) characteristics ( − ∞ , 1) decr -y' +y'' c.c. up x = 1 -27 0 +y'' EVP, min c.c. up (1, 2) incr +y' +y'' c.c. up x = 2 incr +y' 0 PI (2, 4) incr +y' − y'' c.c. down x =4 0 0 0 PI (change in shape, but no change in direction) (4, ∞ ) incr +y' +y'' c.c. up 1 4 − y' +y' +y' min x=4 not critical # no change in direction 2 4 +y'' +y'' − y''...
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This note was uploaded on 02/21/2011 for the course MATH 408C taught by Professor Knopf during the Spring '10 term at University of Texas.

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