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Math Help - Differentiation

  1. #1
    Junior Member Fnus's Avatar
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    Differentiation

    I'd like help with all of the first exercise, and then the two last parts of the last two exercises, 'cause I've done the first parts.
    Hope that made sense.
    Thanks in advance (:
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  2. #2
    Forum Admin topsquark's Avatar
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    Find the equation of the normal line to
    y = \frac{1}{(x^2 + 1)^2}
    at the point
    \left ( 1, \frac{1}{4} \right )

    First we want the value of the slope of the tangent line at this point. So:
    \frac{dy}{dx} = -\frac{4x}{(x^2 + 1)^3}

    At x = 1 this is
    \frac{dy}{dx}_{x = 1} = -\frac{1}{2}

    Now, the line normal to the curve at this point has a slope of -\frac{1}{-\frac{1}{2}} = 2

    So it has the form
    y = 2x + b

    We know this line passes through the point <br />
\left ( 1, \frac{1}{4} \right ), so
    \frac{1}{4} = 2 \cdot 1 + b

    b = -\frac{7}{4}

    Thus the normal line is y = 2x - \frac{7}{4}

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Come now! The second part of number 3 is not a Calculus problem.

    For what values of x is
    \frac{dy}{dx} = \frac{x^2 + 4x - 7}{(x + 2)^2}
    0 or undefined.

    For the first part solve
    \frac{x^2 + 4x - 7}{(x + 2)^2} = 0

    For the second part, consider what values of x make the denominator 0 (which is forbidden.)

    -Dan
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  4. #4
    Junior Member Fnus's Avatar
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    Thanks for running me through the first one, I'm pretty sure I got what you did.

    About the other stuff, though.
    I'm not totally sure how to solve for 0...
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Fnus View Post
    Thanks for running me through the first one, I'm pretty sure I got what you did.

    About the other stuff, though.
    I'm not totally sure how to solve for 0...
    Quote Originally Posted by topsquark View Post
    For the first part solve
    \frac{x^2 + 4x - 7}{(x + 2)^2} = 0
    You're thinking about this too hard.
    \frac{x^2 + 4x - 7}{(x + 2)^2} = 0

    Multiply both sides by (x + 2)^2:
    x^2 + 4x - 7 = 0

    Can you solve this?

    -Dan
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  6. #6
    Junior Member Fnus's Avatar
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    Yep, I can.
    Thanks a ton

    - Frederikke
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