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Homework Help: Urgent Help Needed - Local Minimum/ maximum question

  1. Mar 28, 2012 #1
    Hey forum I gotta submit this in a few hours so if anyone could help me with this quick times, you would really be saving me :P

    1. The problem statement, all variables and given/known data
    Given the following graph of h(x)
    I only need help with part b)
    which asks for the local minimum or maximum points of the graph


    3. The attempt at a solution

    So basically I realize there's a horizontal tangent at the point h(2)

    What I can't decide is if there is neither a minimum nor maximum (my initial thoughts)

    but then one part of my book reads for ANOTHER graph:
    f'(x) is never zero, so the function has no local maximums or minimums

    and we can clearly see that h(x) has a horizontal tangent implying that h'(x) would be zero at h'(2).. so
    is the point [2,h(2)] both a local minimum and a local maximum

    Is that even possible for a point to be both a local maximum and a local minimum?

    if someone could clarify as to why its whichever answer that would be awesome!
    argh please help! :confused:
  2. jcsd
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