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Math Help - need help within 12 hours pre calc

  1. #1
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    need help within 12 hours pre calc

    Hey guys i need help with this question using the formula

    F( x + h) - F ( x )
    -----------------
    h

    The question being:

    F ( x ) = x^1/3

    please with a breif explanation of how its done as well thank you!
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  2. #2
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    Quote Originally Posted by jamman790 View Post
    Hey guys i need help with this question using the formula

    F( x + h) - F ( x )
    -----------------
    h

    The question being:

    F ( x ) = x^1/3

    please with a breif explanation of how its done as well thank you!
    If f(x) = x^{\frac{1}{3}} then f(x + h) = (x + h)^{\frac{1}{3}}.

    You're just substituting x + h where x was.

    So

    \frac{f(x + h) - f(x)}{h} = \frac{(x + h)^{\frac{1}{3}}-x^{\frac{1}{3}}}{h}.
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  3. #3
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    Here is the KEY to this question.
    x^3 - y^3 = (x - y )(x^2 + xy + y^2 ).
    Now, you may not grasp that at first!
    But think about.
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  4. #4
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    I understand that your subing them in but where do you go from there? i mean how do you expand that?...with the perfect cubes formula listed above?..how does that work? there not being cubed there to the ^1/3..sorry im trying to think about it but am confuzzled:|! Wait do you sub a variable?
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  5. #5
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    Hello, jamman790!

    We want the Difference Quotient: . \frac{f(x+h) - f(x)}{h}


    Break it up into three steps:

    (1) Find f(x+h) . . . Replace x with x+h ... and simplify.

    (2) Subtract f(x) . . . Subtract the original function ... and simplify.

    (3) Divide by h . . . Reduce and simplify.



    f(x) \:=\:x^{\frac{1}{3}}

    (1) Find f(x+h)\!:\quad f(x+h) \:=\:(x+h)^{\frac{1}{3}}


    (2) Subtract f(x)\!:\quad f(x+h)-f(x) \;=\;(x+h)^{\frac{1}{3}} - x^{\frac{1}{3}}

    . . .Multiply top and bottom by: . (x+h)^{\frac{2}{3}} + (x+h)^{\frac{1}{3}}x^{\frac{1}{3}} + h^{\frac{2}{3}}

    . . . \frac{(x+h)^{\frac{1}{3}} - x^{\frac{1}{3}}}{1}\cdot \frac{(x+h)^{\frac{2}{3}} + (x+h)^{\frac{1}{3}}x^{\frac{1}{3}} + h^{\frac{2}{3}}} {(x+h)^{\frac{2}{3}} + (x+h)^{\frac{1}{3}}h^{\frac{1}{3}} + h^{\frac{2}{3}}}

    . . . = \;\frac{(x+h) - x}{(x+h)^{\frac{2}{3}} + (x+h)^{\frac{1}{3}}h^{\frac{1}{3}} + h^{\frac{2}{3}} }

    . . . \;=\;\frac{h}{(x+h)^{\frac{2}{3}} + (x+h)^{\frac{1}{3}}h^{\frac{1}{3}} + h^{\frac{2}{3}}}


    (3) Divide by h

    . . . \frac{f(x+h)-f(x)}{h} \;=\;\frac{{\color{red}\rlap{/}}h}{{\color{red}\rlap{/}}h\left[(x+h)^{\frac{2}{3}} + (x+h)^{\frac{1}{3}}h^{\frac{1}{3}} + h^{\frac{2}{3}}\right]} =\;\frac{1}{(x+h)^{\frac{2}{3}} + (x+h)^{\frac{1}{3}}h^{\frac{1}{3}} + h^{\frac{2}{3}}}

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  6. #6
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    when you multiply the top and bottom by that long equation..how did u figure out you needed to multiply it by that?...
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