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Math Help - Slope of tangent line

  1. #1
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    Slope of tangent line

    Find the slopeof the functions graph at the given point.

    f(x)= x / (x-2) point (3,3)

    We have to use the method f(a+h)-f(a) / h to find the answers.
    so I have it down to this and dont know what to do next so h will cancel.

    ((3+h)/(3+h-2) - 3) / h

    can someone please help me to reduce this.
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  2. #2
    Super Member 11rdc11's Avatar
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    just find the your derivative 1st

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

    which ends up being after you simplfy some.

    \lim_{h \to 0} \frac{-2}{x^2 - 4x -2h + xh +4}

    Do you know what to do next?
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  3. #3
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    Quote Originally Posted by 11rdc11 View Post
    just find the your derivative 1st

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

    which ends up being after you simplfy some.

    \lim_{h \to 0} \frac{-2}{x^2 - 4x -2h + xh +4}

    Do you know what to do next?
    ok backing up a step..how did you get from \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

    to
    \lim_{h \to 0} \frac{-2}{x^2 - 4x -2h + xh +4}

    basically my problem is going from ((3+h)/ (3+h -2)) -3 / h to what you have. How did you simplify the numerator to get -2?
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  4. #4
    Super Member 11rdc11's Avatar
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    \lim_{h \to 0}\frac{\frac{x+h}{x + h -2} -\frac{x}{x-2}}{h}

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


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

    Can you take it from here?
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  5. #5
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    Quote Originally Posted by 11rdc11 View Post
    \lim_{h \to 0}\frac{\frac{x+h}{x + h -2} -\frac{x}{x-2}}{h}

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


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

    Expand and add like terms after
    Thank you so much. I understand how to do the problems, my simplification skills just aren't as up to date as I would like them to be. That helped me a lot thank you again.
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