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Determining Extrema

  1. Apr 5, 2005 #1

    I am doing a question about curve sketching and determining extrema and just need some clarification. Here is the question:

    Determine the extreme values of the function f(x) = x^2 - 8x + 9, where
    -1 is greater than or equal to x is less than or equal to 5.

    This is what I have done so far:

    I decided to check for stationary points, as extreme values may occur at f'(0)=0.

    f'(x) = 2x-8
    2x-8 = 0
    x = 4

    f(4) = 4^2 - 8(4) +9 = -7
    (4,-7) may be a max, min or neither.

    f(3.9) = (3.9)^2 - 8(3.9)+9 = -6.99
    f(4.1) = (4.1)^2 - 8(4.1)+9 = -6.99

    Does this mean that this point cannot be used in determining the absolute minimum? I am totally lost at this point. I was going to use the endpoints given to figure out the maximum, but I'm not sure if that is an acceptable method. Thanks for any help you can give me.
  2. jcsd
  3. Apr 5, 2005 #2
    You can use the endpoints of the interval as well as x = 4. You are allowed to use the endpoints because they are included in the interval.
  4. Apr 5, 2005 #3


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    The function is continuous on the whole domain.It's a parabola.The theory says that the sign of "a" (=1,in this case) decides the nature of the extremum...In this case,it's a minimum...

    That's all there's to it.

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