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Unformatted text preview: ´ (b) Determine all (vertical and horizontal) asymptote(s) of f ( x ). (c) Find f ′ ( x ) and f ′′ ( x ). f ′ ( x ) = ± ² ³ ´ and f ′′ ( x ) = ± ² ³ ´ . (d) Write down all critical point(s) of f ( x ): ± ² ³ ´ . (e) Find the interval(s) on which f is increasing and also the interval(s) on which f is decreasing. f ( x ) is increasing on the interval(s) ± ² ³ ´ and f ( x ) is decreasing on the interval(s) ± ² ³ ´ . 4 (f) Find the interval(s) on which f is concave up and also the interval(s) on which f is concave down. f ( x ) is concave up on the interval(s) ± ² ³ ´ and f ( x ) is concave down on the interval(s) ± ² ³ ´ . (g) Write down all inﬂection point(s) of f ( x ): ± ² ³ ´ . (h) Write down all root(s) of f (all x such that f ( x ) = 0): ± ² ³ ´ (i) Sketch f ( x ). 5 This page intentionally left blank for scratch work 6...
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 Fall '10
 LUXNU
 Math, Calculus, Derivative, mobile phones, Convex function, cos x cos, sin x cos

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