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Math Help - [SOLVED] derivative

  1. #1
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    [SOLVED] derivative

    y=x^2/x+1 find all x values at which the tangent line is parallel to the line y=x

    after you find the quotient of the problem how do you determine if its parallel to y=x

    im at x^2+2x-1/x^2+2x+1
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by vinson24 View Post
    y=x^2/x+1 find all x values at which the tangent line is parallel to the line y=x

    after you find the quotient of the problem how do you determine if its parallel to y=x

    im at x^2+2x-1/x^2+2x+1
    I get that \frac{\,dy}{\,dx}=\frac{2x(x+1)-x^2}{(x+1)^2}=\frac{x^2+2x}{(x+1)^2}.

    Now find a x that causes \frac{\,dy}{\,dx}=1

    Thus, \frac{x^2+2x}{x^2+2x+1}=1

    Can this ever be true?

    --Chris
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    sorry the numerator is x^2+1 i forgot to put the one in
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by vinson24 View Post
    sorry the numerator is x^2+1 i forgot to put the one in
    It changes things a little:

    \frac{\,dy}{\,dx}=\frac{2x(x+1)-(x^2+1)}{(x+1)^2}=\frac{x^2+2x-1}{(x+1)^2}

    Find the value of x that causes \frac{\,dy}{\,dx}=1

    This implies that \frac{x^2+2x-1}{(x+1)^2}=1\implies x^2+2x-1=x^2+2x+1

    Can this ever be true?

    --Chris
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  5. #5
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    does that equal zero
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    It changes things a little:

    \frac{\,dy}{\,dx}=\frac{2x(x+1)-(x^2+1)}{(x+1)^2}=\frac{x^2+2x-1}{(x+1)^2}

    Find the value of x that causes \frac{\,dy}{\,dx}=1

    This implies that \frac{x^2+2x-1}{(x+1)^2}=1\implies x^2+2x-1=x^2+2x+1

    Can this ever be true?

    --Chris
    Quote Originally Posted by vinson24 View Post
    does that equal zero
    Um...no.

    x^2+2x-1=x^2+2x+1\implies -1=1

    This is a false statement. Thus, there is no tangent line to this graph parallel to the line y=x.

    --Chris
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  7. #7
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    ooh because in the back of the book the answer it gave was 0

    along those lines if you wanted dy/dx to pass through the orgin what does it equal to
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  8. #8
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    i think by zero it means there isnt any thanks alot
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