Quiz 6 solutions

Quiz 6 solutions - 2 2 12 3 3 4 3 2 2 f x x x x x ′...

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QUIZ 6 SOLUTIONS SHOW ALL WORK 1. Find the limits: USE L’HOPITAL’S RULE a) 0 0 sin 2 2cos2 0/ 0; lim lim 2/5 [ , ] sin5 5cos5 x x x x formis usechainrule top and bottom x x = = b) Form is / ∞ ∞ ( ( 29 2 2 2 0 0 0 0 ln sin cos /sin cot tan 1 lim lim lim lim 1 ln tan sec / tan sec sec x x x x x x x x x x x x x x + + + + = = = = 2. Find a) intervals on which f is increasing, b) intervals on which f is decreasing, c) open intervals on which f is concave up, d) intervals on which f is concave down and e) x-coordinates of all inflection points and SHOW SIGN GRAPHS FOR and f f ′′ : ( 3 5 12 y x x f x
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Unformatted text preview: 2 2 12 3 3 4 3 2 2 f x x x x x ′ =-=-= +-so the critical points are at x = 2, x = - 2 Sign graph shows f is > 0 on [-2, 2] [hence f increasing there: a)] and < 0 on ( ] [ 29 , 2 2, and-∞ -+∞ [b)] ( 29 6 f x x ′′ = -which is > 0 on ( ] ,0-∞ [hence graph is concave up there: c)]and < 0 on [ 29 0, +∞ [hence graph is concave down there: d)] and since f ′′ changes sign at x = 0, that is the x-coordinate of the inflection point....
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