Connections Between Function Features And Limits

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Connections Between Function Features And Limits

What does different limits information tell us about the features of a function?


Questions and Answers
  • 1. 
    Select all the places to look for extreme points (maxima, minima):
    • A. 

      Where the instantaneous rate of change is zero

    • B. 

      Where the instantaneous rate of change does not exist

    • C. 

      At the endpoints of the interval of interest

    • D. 

      Where the function value is zero

  • 2. 
    Which of the following must be true if a function f(x) does not have a minimum on an interval [a,b].
    • A. 

      F(x) must approach negative infinity somewhere in the interval [a,b]

    • B. 

      F(x) must have a discontinuity on [a,b]

    • C. 

      F(a) must be greater than f(b)

    • D. 

      F(x) must have a maximum on the interval [a,b]

  • 3. 
    Which existence theorem allows use to use guess-and-check to solve equations which can be written in the form F(x) = 0 for a continuous function F?
    • A. 

      The Intermediate Value Theorem

    • B. 

      The Mean Value Theorem

    • C. 

      The Extreme Value Theorem

    • D. 

      Rolle's Theorem

  • 4. 
    Select all the correct statements about extreme points of the function in the graph.
    • A. 

      The absolute minimum value is 0.

    • B. 

      The absolute maximum value is 14/3.

    • C. 

      There is a relative minimum between x=–5 and x=–4.

    • D. 

      There is one point which is a relative maximum where the instantaneous rate of change is zero.

    • E. 

      The instantaneous rate of change does not exist at x=–3 and there is a relative maximum there.

    • F. 

      (1,1) is a relative maximum point.

    • G. 

      The left end point is a relative maximum.

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