Exam 3: Applications of the Derivative

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​Approximate the critical numbers of the function shown in the graph and determine whether the function has a relative maximum,a relative minimum,an absolute maximum,an absolute minimum,or none of these at each critical number on the interval shown. ​ ​Approximate the critical numbers of the function shown in the graph and determine whether the function has a relative maximum,a relative minimum,an absolute maximum,an absolute minimum,or none of these at each critical number on the interval shown. ​   ​ ​

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​Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by ​Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by   ,   ,where x is the number of machines used.What is the minimum average cost? ​ , ​Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by   ,   ,where x is the number of machines used.What is the minimum average cost? ​ ,where x is the number of machines used.What is the minimum average cost? ​

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