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Homework Help: Relative extrema problem for Essentials of Calculus

  1. Jul 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the relative extrema of each function, if they exist. List each extremum along with the x-value at which it occurs. Then sketch a graph of the function.

    25. f(x)=1-x2/3

    2. Relevant equations

    3. The attempt at a solution

    f prime of (x)= -2/3x-1/3

    -2/3x-1/3= 0

  2. jcsd
  3. Jul 12, 2010 #2


    Staff: Mentor

    There are no solutions to the equation f'(x) = 0. Extreme values can occur at points other than where the deriviative is zero. What are these other points?
  4. Jul 12, 2010 #3
    Thanks for the help, I figured it out.

    It was (x)=0 for f'(x) , idk why I couldn't see that. so when i put that in the original equation i got 1. So the x point was (0,1) . And then I found the remaning points on the graph and it was correct with the back of the book answer.

    Thank you

    If i have another questions, can i just ask here or should i make a new topic? It's the same type of questions just another problem?
    Last edited: Jul 12, 2010
  5. Jul 12, 2010 #4


    Staff: Mentor

    But x = 0 is not a solution of f'(x) = 0, and that's what you were looking for. Do you understand why x = 0 is an extreme point?
    Please start a new thread.
  6. Jul 12, 2010 #5
    No i don't know what you mean. I came back from class but I remember this problem still. (0,1) was the realtive maximum at least I am fairly sure. I don't need a solution, i just needed the relative extrema which is (0,1) and then sketch... thats right, isn't it?
  7. Jul 13, 2010 #6


    Staff: Mentor

    Yes, (0, 1) is the maximum point. An extreme point of a function f can occur at any of the following:
    1. Points at which f'(x) = 0
    2. Points in the domain of f at which f' is undefined
    3. Endpoints of the domain of f

    The work you showed in your first post was toward the first point above, but for your function, there are no values x for which f'(x) = 0. It wasn't clear to me that you understood where to look for extreme values.
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