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Unformatted text preview: < f (1) < f 00 (1) 6. f (1) < f 00 (1) < f (1) Explanation: (i) Whether the point (1 , f (1)) lies above or below the xaxis determines the sign of f (1), and f (1) = 0 if the point lies on the xaxis. (ii) Whether the graph of f is increasing or decreasing at the point (1 , f (1)) determines the sign of f (1), and f (1) = 0 when the tangent line to the graph is horizontal at (1 , f (1)). (iii) Whether the graph of f is concave up or concave down at the point (1 , f (1)) determines the sign of f 00 (1), and if the graph is changing concavity at (1 , f (1)), then f 00 (1) = 0. In the graph above, therefore, the inequalities f 00 (1) < f (1) < f (1) are satised. keywords: concavity, decreasing, increasing, graph 012 (part 1 of 1) 10 points Find all intervals on which f ( x ) = x 2 ( x + 1) 3 is increasing....
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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
 CLARK,C.W./HOY,R.R
 Critical Point, Quotient Rule

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