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Math Help - Related Rate

  1. #1
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    Related Rate

    please help me...

    1. Consider the function .

    The absolute maximum value is: ???
    and this occurs at ???

    The absolute minimum value is: ???
    and this occurs at ??

    2. Consider the function .

    Find the absolute minimum value of this function.
    Answer: ??

    find the absolute maximum value of this function.
    Answer: ??

    Find the absolute maximum and absolute minimum values of the function
    on the interval .
    Absolute maximum = ???

    Absolute minimum = ????
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  2. #2
    MHF Contributor matheagle's Avatar
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    In these you need to check the endpoints and where f'=0.
    That's rather straight forward.
    So in (1) f'=0 at x=0.
    So you just need to compare f(0), f(-5) and f(2).
    But clearly, since this is an 'upside down' parabola the max occurs at x=0 and that value is 4.
    The min occurs at the endpoints, just comapre those two.
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  3. #3
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by Kayla_N View Post
    please help me...

    1. Consider the function .

    The absolute maximum value is: ???
    and this occurs at ???

    The absolute minimum value is: ???
    and this occurs at ??

    2. Consider the function .

    Find the absolute minimum value of this function.
    Answer: ??

    find the absolute maximum value of this function.
    Answer: ??

    Find the absolute maximum and absolute minimum values of the function
    on the interval .
    Absolute maximum = ???

    Absolute minimum = ????
    To find minimum and maximum values you need to take the derivative and then use a sign chart to see where the sign of the derivative changes from - to + OR + to - on the given interval.
    When the sign of f' changes, the graph of f will have a max or min.
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  4. #4
    MHF Contributor matheagle's Avatar
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    In 2 you can use calculus also, but it's real easy to complete the square.
    x^4-32x^2+5=x^4-32x^2+256-256+5=(x^2-16)^2-251.
    Hence the abs min occurs when x=-4 or 4, value is -251.
    BUT you need to make sure these are x's in your region.
    Well -4 isn't, so abs min occurs at x=4, now check for enpoints to get your max.
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  5. #5
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    ok 3 f'(x)= (8x+4)(4)-4x(8) / (8x+4)^2

    maximum= 4/9
    minimum= 1/3
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  6. #6
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Kayla_N View Post
    ok 3 f'(x)= (8x+4)(4)-4x(8) / (8x+4)^2

    maximum= 4/9
    minimum= 1/3

    set f'=0
    and look at f at your two endpoint, ttyl
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