1 c Kathryn Bollinger October 29 2010 Week In Review 7 4 2 4 3 4 6 1 Use the graph below to determine the absolute and local maximum and minimum values of f if any exist and where each of these values occurs 7 f x 5 2 Given f x is a continuous function with f x p x 2 x 3 4 x 5 3 where p is a function that is always positive determine critical numbers of f x intervals where f x is increasing or decreasing and any values of x where local extrema of f x will occur c Kathryn Bollinger October 29 2010 2 3 Consider f x 4x x4 Use calculus to determine the a Critical numbers of f x b Local extrema of f x using both the First Derivative Test and Second Derivative Test if possible c Interval s where f x is concave up or concave down d Inflection points of f x 3 c Kathryn Bollinger October 29 2010 4 Determine the absolute extrema if any exist of each function on the indicated intervals a f x x3 3x2 24x 5 i On 0 6 ii On 3 0 iii On b f x 12 x i On 5 5 ii On 10 0 9 x c Kathryn Bollinger October 29 2010 5 For each function below use calculus to find the following information Then sketch each function a Domain of f x b Intercepts c Vertical and Horizontal Asymptotes Holes d All critical numbers e All intervals where f x is increasing decreasing f Any points of local extrema g All intervals where f x is concave up concave down h Any inflection points A f x x4 6x2 5 4 c Kathryn Bollinger October 29 2010 B f x x2 1 16 5 c Kathryn Bollinger October 29 2010 C f x 3 2x 5 6 c Kathryn Bollinger October 29 2010 D f x ex e x 7 c Kathryn Bollinger October 29 2010 E f x ln x x 8 c Kathryn Bollinger October 29 2010 9 6 From a 27 inch by 9 inch piece of cardboard square corners are cut out so that the sides can be folded up to form a box with no top Use calculus to determine the maximum volume the box will be able to hold c Kathryn Bollinger October 29 2010 10 7 A farmer has 1200 m of fencing He wants to enclose a rectangular field bordering a river with no fencing needed along the river a Use calculus to find the fence dimensions that will maximize the enclosed area b What is the maximum enclosed area
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