1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    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.)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Finding extreme values
  1. Extreme Values (Replies: 3)

  2. Extreme values (Replies: 1)