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Math Help - Absolutes

  1. #1
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    Absolutes

    Find the absolute maximum and minimum values of the following function on the interval [1,3]

    <br />
f(x) = \frac{4x^2+9}{x}<br />

    Do i make a table of values or what do i do?
    Thanks to everyone who helps
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  2. #2
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    what do you know about derivatives? ... i.e., what they can tell you about the behavior of a function.
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  3. #3
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    Quote Originally Posted by qzno View Post
    Find the absolute maximum and minimum values of the following function on the interval [1,3]

    <br />
f(x) = \frac{4x^2+9}{x}<br />

    Do i make a table of values or what do i do?
    Thanks to everyone who helps
    The absolute maximum and minimum will either be where the derivative is 0, or on the endpoints.

    The endpoints are

    f(1) = 13 and f(3) = 15

    The derivative is

    f'(x) = \frac{4x^2 - 9}{x^2} (use the Quotient rule).

    Set this equal to 0 and solve for x.

    0 = \frac{4x^2 - 9}{x^2}

    0= 4x^2 - 9

    0 = (2x + 3)(2x - 3)

    2x+3 = 0 or 2x - 3= 0

     x = -\frac{3}{2} or x = \frac{3}{2}.


    Substitute these values back into f(x) to determine their corresponding y-values.

    f(\frac{3}{2}) = 12, f(-\frac{3}{2}) = -12.


    So the absolute maximum is 15 which occurs at x = 3, and the absolute minumum is -12 and occurs at x = -\frac{3}{2}.
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  4. #4
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    how is x = -\frac{3}{2} on the interval [1,3] ?
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  5. #5
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    Quote Originally Posted by qzno View Post
    how is x = -\frac{3}{2} on the interval [1,3] ?
    Oops - my mistake :P.

    That means the minimum is actually 12 and occurs at x = \frac{3}{2}
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  6. #6
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    ohh ok thanks !
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