Features Of Polynomials

10 Questions | Total Attempts: 123

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Features Of Polynomials

. What do the features of f' and f'' tell you about the original funciton f?


Questions and Answers
  • 1. 
    For a polynomial P(x) defined on an interval [a,b], where do you need to check for minima and maxima? 
    • A. 

      Wherever P(x) = 0

    • B. 

      Wherever P'(x) = 0

    • C. 

      Wherever P''(x) = 0

    • D. 

      At x = a and x = b

  • 2. 
    Statement: An absolute (global) maximum is also a relative (local) maximum.
    • A. 

      True

    • B. 

      False

  • 3. 
    Statement: Relative (local) extremes cannot occur at endpoints unless the slope of the tangent line at the endpoint is zero.
    • A. 

      True

    • B. 

      False

  • 4. 
    Statement:  A point of inflection is found at any location where the second derivative of a function is zero.
    • A. 

      True

    • B. 

      False

  • 5. 
    Statement:  At a location where the first derivative of a function is zero, the function may have a local minimum, a local maximum, or a point of inflection.
    • A. 

      True

    • B. 

      False

  • 6. 
    Statement:  The slope of the tangent line at a point of inflection is always zero.
    • A. 

      True

    • B. 

      False

  • 7. 
    Consider the polynomial f(x) and the sign line shown for its derivative f'(x). Which statement best describes the relative extrema of f?
    • A. 

      The function f has relative minima at –2 and 5/2, and a relative maximum at 0

    • B. 

      The function f has a relative minimum at 0 and a relative maximum at 5/2

    • C. 

      The function f only has one relative extreme: a maximum at –2

    • D. 

      The function f has a relative maximum at 0 and a relative minimm at 5/2

  • 8. 
    Consider the polynomial f(x) and the sign line shown for its derivative f'(x). Which statement about increasing vs. decreasing is true?
    • A. 

      The function f is increasing on the interval [–1,1]

    • B. 

      The function f is decreasing on the inverval [–1,1]

    • C. 

      The function f is decreasing on the interval [0,5/2]

    • D. 

      The function f is overall an increasing function

  • 9. 
    Consider the polynomial f(x) and the sign line shown for its derivative f'(x). Which statement about inflection points of f is definitely true?
    • A. 

      The function f does not have any inflection points

    • B. 

      The function f has an inflection point at –2 and possible inflection points at 0 and/or 5/2

    • C. 

      The function f has an inflection point at –2 and potentially other inflection points, but NOT at 0 or 5/2

    • D. 

      The function f has exactly four inflection points