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The number of new businesses established in the US since 1990 can be modeled by the...

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Advance Math

The number of new businesses established in the US since1990 can be modeled by the functionNx=110.8x^3-5305.5x^2+76,701x+332,892 where x = 0 represents 1990and the domain is [0, 25].   

  1. According to the model, about how many new businesses wereestablished in 2011? Don’t forget to label and interpret theanswer.   
  1. What was the average rate of change in the number of newbusinesses established between 2000 and 2010? Don’t forget to labeland interpret the answers.  
  1. What is the instantaneous rate of change in the number of newbusinesses established in 2011? Remember to label and interpret theanswer.   
  1. Consider the year 2015 (x = 25). Evaluate D(25),D’(25), and D’’(25). Label and interpret the meaning of eachanswer.

  1. Use the First Derivative Test to determine the extrema of thefunction on the given domain. Classify as max/min andabsolute/relative. For what intervals does the functionincrease/decrease? Please label and interpret each answer in thecontext of this problem.

6. Use the Second Derivative Test to discuss the concavity ofthis function on the given interval. What is the POI? Interpret themeaning of the POI in the context of thisproblem.           

    

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