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Math Help - absolute max and min

  1. #1
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    Talking absolute max and min

    find the absolute maximum and absolute minimum (if any) of the given function on the specified interval:

    f(x)=x^2 + 4x + 5; -3=<x=<1

    the book has:

    max (1, 10)
    min (-2, 1)

    The book is a terrible resource, its not as clear as someone explaining it to you...as always I appreciate any help...thanks!
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  2. #2
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    Find your second derivative, then find for what values of x your second derivative equals 0. Calculate the f(x) with the values of x you find, the highest f(x) is your absolute maximum and the lowest is your absolute minimum.
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by lisa1984wilson View Post
    find the absolute maximum and absolute minimum (if any) of the given function on the specified interval:

    f(x)=x^2 + 4x + 5; -3=<x=<1

    the book has:

    max (1, 10)
    min (-2, 1)

    The book is a terrible resource, its not as clear as someone explaining it to you...as always I appreciate any help...thanks!
    This one's easy cause u konw that this is a parabola that opens upward having only one minimum, You don't need calc, but if u insissssst.........

    f'(x)=0 will give us all relative max/min.

    but, it dont tell us nuttin bout if its a min or a max.....but the second derivative duzzzzzzzzzzzzz..................

    • x = a is a locally a minimum if f"(a) > 0,
    • x = a is a locally a maximum if f"(a) < 0; and
    So let's do it

    f'(x)=2x+4=0\Longleftrightarrow{x=-2}

    looks like we got ourselves only one max/min, but which one is it. I don't knoooooooooowwwwwwwww!!!!!!!!

    Wait a sec.... Ill use the second derivative.

    f''(x)=2 and 2>0! Its a minimum. YYAAAAAAAYYYYYYYYY!

    its in the interval [-3,1] too! yyyaaaaaaaaaaaaaaaayyyyyyyyy!!!!


    PEACE OUT!

    ps We only found the min. The max can be found by evaluating \lim_{x\to{-3^+}}f(x) and \lim_{x\to{1^-}}f(x) and see whichuns bigger.
    Last edited by VonNemo19; May 29th 2009 at 01:47 PM. Reason: forgot something
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