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Unformatted text preview: f ( x ) = (6 + x )(4 x ) ( x 2 + 24) 2 = 0 . Thus the critical points of f are x = 6 and x = 4. To classify these critical points we use the First Derivative Test. But the sign of f de-pends only on the numerator, so it is enough, therefore, to look only at a sign chart for (6 + x )(4 x ): 6 4 + From this it follows that f is decreasing on ( , 6), increasing on ( 6 , 4), and de-creasing on (4 , ). Consequently, f has a local maximum at x = 4 . keywords: local maximum, local minimum, critical point, quotient rule, First Derivative Test, rational function 016 10.0 points Find the interval(s) where f ( x ) = 2 3 x 4 1 3 x 3 3 x 2 5 x + 1...
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This note was uploaded on 02/14/2012 for the course MATH 408 K taught by Professor Clark,c.w./hoy,r.r during the Spring '08 term at University of Texas at Austin.
- Spring '08