Unformatted text preview: e. Identify any local extrema of the function. f. Over what intervals is the function concave upward? g. Over what intervals is the function concave downward? h. Give the coordinates of any inflection points. 3. Suppose that ) ( x f is continuous on [0,4], 1 ) ( = f , and 5 ) ( 2 ≤ ′ ≤ x f for all x in (0,4). Show that 21 ) 4 ( 9 ≤ ≤ f . 4. Sketch the graph of a continuous function satisfying: f(0)=2; f(2)=f(2)=1;f ‘(0)=0; f ‘ (x)> 0 if x < 0; f ‘ (x) < 0 if x> 0; f “(x) > 0 if x < 2; f “ (x) > 0 if x > 2. 5. Given f(x) = cos x + sin x. Sketch a graph of f(x) indicating all relative extrema and inflection points. Show all work....
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 Spring '08
 Zhang
 Critical Point, Derivative, Fermat's theorem

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