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Math Help - Curve Sketching Tangents, etc Question

  1. #1
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    Curve Sketching Tangents, etc Question

    For the first question, I get x=1, -1 for critical points. The interval of increase is -1<x<1. The local extrema are (-1,-1/2) and (1,1/2)
    The H.A is y=0 and the curve crosses it at (0,0)? I could be wrong, here's the question differentiated-f'(x)=1-x^2/(1-x^2)^2

    For the second one, I get the slope to equal 1/-5 and y intercept to be -14/5?

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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by SportfreundeKeaneKent View Post
    For the first question, I get x=1, -1 for critical points. The interval of increase is -1<x<1. The local extrema are (-1,-1/2) and (1,1/2)
    The H.A is y=0 and the curve crosses it at (0,0)? I could be wrong, here's the question differentiated-f'(x)=1-x^2/(1-x^2)^2

    For the second one, I get the slope to equal 1/-5 and y intercept to be -14/5?

    yup. everything is correct except the derivative formula you have for the first one, but i'm sure that was just a typo and you actually did it correctly...just to make sure, you mind telling me the correct function for f'(x)?
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  3. #3
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    curve sketching

    The curve is shown as follows:
    Attached Thumbnails Attached Thumbnails Curve Sketching Tangents, etc Question-02jun2007.jpg  
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  4. #4
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    Tangent to the ellipse

    Tangent to the ellipse
    Attached Thumbnails Attached Thumbnails Curve Sketching Tangents, etc Question-03jun2007.jpg  
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  5. #5
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    It goes from f(x)=x/1+x^2 to being differentiated to

    f'(x)=(1-x^2)-x(2x)/(1+x^2)^2
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by SportfreundeKeaneKent View Post
    It goes from f(x)=x/1+x^2 to being differentiated to

    f'(x)=(1-x^2)-x(2x)/(1+x^2)^2
    that is incorrect, and you should put brackets around the numerator

    it would be:

    f'(x) = \frac {(1 + x^2) - x(2x)}{ \left(1 + x^2 \right)^2} = \frac {1 - x^2}{ \left(1 + x^2 \right)^2} = \frac {(1 + x)(1 - x)}{ \left( 1 + x^2 \right)}
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