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Finding extreme values

  1. Oct 21, 2006 #1
    So I know how to find extreme value when it is a closed interval
    for example

    f(x) = x^2 - 1, -1 <= x <= 2
    in this i would first find the critical point. and then i would compare f(critical point) and f(-1) and f(2) and then find the maximum and minimum values that way.

    but my question is how to find extreme values when it is not a closed interval. Right now what I am doing is I plot the graph on my calculator and look at the max and the minimum values. But i am sure thats not the correct way of doing it. I'm sure there is some way to find the max and the min algebraically.

    here is an example of a problem without closed intervals
    f(x) = 2x^2 - 8x + 9

    Thanks in advance
  2. jcsd
  3. Oct 24, 2006 #2
  4. Oct 25, 2006 #3
    Have you tried the second derivative test?
  5. Oct 25, 2006 #4


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    Science Advisor

    A continuous function does not necessarily HAVE a maximum or minimum on an open interval. Start in exactly the way you did for a closed interval. Find the critical points, evaluate at those critical points and the end points. The difference is: if the value at one end point is larger than at any of the critical points, the function does NOT have a maximum in that interval. If the value at one end point is smaller than at any of the critical points, the function does NOT have a minimum in that interval.

    (I'm assuming that the function is continuous at both end point.)
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