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Unformatted text preview: f ‘ (x) is decreasing implies f is concave down If concavity switches at a point, it is called and inflection point. Easiest example: 3 ) ( x x f = 2 nd Derivative Test Suppose f ‘’ is continuous near c. a) if f ‘(c) = 0 and f ‘’(c) > 0 then f has a local min. at x = c b) if f ‘(c) = 0 and f ‘’(c) < 0 then f has a local max. at x = c Example: Go back to the function in the above example 1 4 ) ( 4--= x x x f And discuss concavity and inflection points. More Examples: Find all vertical and horizontal asymptotes. Find the interval of increase or decrease. Find the local maximum and minimum values. Fin the intervals of concavity and the inflection points. Use the information to sketch a graph. 1. #30 2 2 ) 2 ( ) (-= x x x f 2. #40 x e x x f-= 2 ) (...
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