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Math Help - need help with algebra finding derivative

  1. #1
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    need help with algebra finding derivative

    Show that the slope of y = x^3 - 3x + 3 at any x is 3x^2 - 3

    A=delta (dont know how to do delta)

    im doing it using this method
    ( (x+Ax)^3 - 3(x+Ax) + 3 ) - ( x^3 - 3x + 3 ) / ( (x+Ax) - x )

    i simplify and get Ax^2 + 3xAx + 3x^2 - 6x
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by stones44 View Post
    Show that the slope of y = x^3 - 3x + 3 at any x is 3x^2 - 3

    A=delta (dont know how to do delta)

    im doing it using this method
    ( (x+Ax)^3 - 3(x+Ax) + 3 ) - ( x^3 - 3x + 3 ) / ( (x+Ax) - x )

    i simplify and get Ax^2 + 3xAx + 3x^2 - 6x
    where did 6x come from?

    you simplified something wrong. expanding everything, you should get:

    \lim_{\Delta x \to 0} \frac {x^3 + 3x^2(\Delta x) + 3x(\Delta x)^2 + (\Delta x)^3 - 3x - 3 \Delta x + 3 - x^3 + 3x - 3}{\Delta x}

    now cancel what is to be canceled, simplify as much as possible, and take the limit
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    where did 6x come from?

    you simplified something wrong. expanding everything, you should get:

    \lim_{\Delta x \to 0} \frac {x^3 + 3x^2(\Delta x) + 3x(\Delta x)^2 + (\Delta x)^3 - 3x - 3 \Delta x + 3 - x^3 + 3x - 3}{\Delta x}

    now cancel what is to be canceled, simplify as much as possible, and take the limit
    doesnt -3(x+Ax) = -3x + -3Ax ? and then the other -3x so -6x
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  4. #4
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    let h = \Delta x

    f(x) = x^3 - 3x + 3

    f(x+h) = (x+h)^3 - 3(x+h) + 3

    \lim_{h \to 0} \frac{(x+h)^3 - 3(x+h) + 3 - (x^3 - 3x + 3)}{h}

    \lim_{h \to 0} \frac{x^3 + 3x^2h + 3xh^2 + h^3 - 3x - 3h + 3 - (x^3 - 3x + 3)}{h}

    now, clean it up and finish finding the limit which will give you the derivative of f.
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  5. #5
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    i figured what i did wrong

    ok so i cleaned it up i have

    3x^2 + 3xAx + Ax^2 - 3

    shouldnt i end up with (3x^2 - 3) +Ax ?
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by stones44 View Post
    doesnt -3(x+Ax) = -3x + -3Ax ? and then the other -3x so -6x
    what other -3x? the only other 3x is +3x
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  7. #7
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    yeah i see what i did

    but i still dont have the answer do i? look at my post above yours
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by stones44 View Post
    yeah i see what i did

    but i still dont have the answer do i? look at my post above yours
    nope, you should end up with 3x^2 + 3x (\Delta x) + (\Delta x)^2 - 3

    and if we let \Delta x \to 0 ...?
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