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Math Help - derivative function

  1. #1
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    derivative function

    Consider the function .

    This function has an absolute minimum value equal to



    and an absolute maximum value equal to
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  2. #2
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    Re: derivative function

    what have you done with this problem?
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  3. #3
    Senior Member x3bnm's Avatar
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    Re: derivative function

    Absolute max or min is where first derivative is zero.

    f(x) =& 2x^3 + 9x^2 -168x + 3


    \begin{align*} \frac{df}{dx} =& 6x^2 + 18x -168 = 0 \\ &x^2 + 3 x - 28 = 0.......\text{[after dividing both sides by } 6 \text{ ]}\\ &(x + 7)(x - 4) = 0......\text{[after factorization]}\end{align*}

    So absolute max or min can be at x = -7 or x = 4. But to find out which one which you plug-in the values into the function and find out which one's larger than the other.

    Now plug-in x = -7 and separately x = 4 into f(x) you'll find that f(-7) > f(4)
    The function has absolute max at x = -7

    And has absolute min at x = 4

    You can check it in the following graph to be sure:

    derivative function-function_graph.jpg
    Last edited by x3bnm; November 29th 2012 at 07:04 PM.
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  4. #4
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    Re: derivative function

    Quote Originally Posted by x3bnm View Post
    Absolute max or min is where first derivative is zero.

    f(x) =& 2x^3 + 9x^2 -168x + 3


    \begin{align*} \frac{df}{dx} =& 6x^2 + 18x -168 = 0 \\ &x^2 + 3 x - 28 = 0.......\text{[after dividing both sides by } 6 \text{ ]}\\ &(x + 7)(x - 4) = 0......\text{[after factorization]}\end{align*}

    So absolute max or min can be at x = -7 or x = 4. But to find out which one which you plug-in the values into the function and find out which one's larger than the other.

    Now plug-in x = -7 and separately x = 4 into f(x) you'll find that f(-7) > f(4)
    The function has absolute max at x = -7

    And has absolute min at x = 4

    You can check it in the following graph to be sure:

    Click image for larger version. 

Name:	function_graph.jpg 
Views:	2 
Size:	12.7 KB 
ID:	25984
    It should be pointed out that in general, absolute maxima and minima could lie at turning points (where the first derivative is 0) OR at endpoints of the function.
    Thanks from x3bnm
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  5. #5
    Senior Member x3bnm's Avatar
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    Re: derivative function

    Quote Originally Posted by Prove It View Post
    It should be pointed out that in general, absolute maxima and minima could lie at turning points (where the first derivative is 0) OR at endpoints of the function.
    Good point Prove It. Thanks for that.
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