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Maxima and Minima of a function

  1. Jan 9, 2009 #1
    Are there any analytical techniques to do this besides the Derivative Test?
  2. jcsd
  3. Jan 10, 2009 #2


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    There is no general method except by checking where the derivitive is 0 (or does not exist). For some functions, there are other ways. For example we can always find minima and maxima for quadratic functions by completing the square.
  4. Jan 10, 2009 #3
    I see. Thanks for that.
  5. Jan 11, 2009 #4
    But there is also possibility to estimate. If you solve some elementary function, for example:
    You can transform it to form:
    So now you are able to find a minimum:
  6. Jan 11, 2009 #5
    Yes, but my function is far too complex/tedious to do either way. An expression for the min and max has been found though proving it is too difficult for me.
  7. Jan 11, 2009 #6
    Well if you are working with quadratics a lot you should know that the min/max is going to be at [tex] \left(\frac{-b}{2a}, f\left(\frac{-b}{2a}\right)\right)[/tex]
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