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Essentials of Calculus use a calculator to estimate any extrema

  1. Jul 26, 2010 #1
    1. The problem statement, all variables and given/known data


    Use a calculator to estimate any extrema of this function:
    f(x)=5x^3-30x^2+45x+5(sqrt(x))

    2. Relevant equations



    3. The attempt at a solution

    I don't know how to find it using a calculator.

    f'(x)= 15x^2-60x+45+(5/2)x^(-1/2)
     
  2. jcsd
  3. Jul 27, 2010 #2

    HallsofIvy

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    Staff Emeritus
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    If your calculator is a graphing calculator, graph y= f'(x) and see where it crosses the x- axis. Another method of solving such an equation is to use a "Newton's method" or some other numerical method.
     
  4. Jul 27, 2010 #3
    Since you are estimating, you can simply graph f(x) and look for peaks (maxes), troughs (mins), and where the graph changes concavity (inflection points; though most books do not consider this an extremum). The derivative is not really needed, unless you want a more accurate estimate.
     
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