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Math Help - Finding the Point of Inflection

  1. #1
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    Finding the Point of Inflection

    Hi

    I need help on the following question:

    1) Find the exact values of the x-coordinates of the points of inflection on the graph of y=2x^4+4x^3-x^2+7x-1

    Ok this is what i have done:
    \frac{dy}{dx} = 8x^3 + 12x^2 - 2x +7

    \frac{d^2y}{dx^2} = 24x^2+24x-2

    make \frac{d^2y}{dx^2} = 0

    Now i tried using the quadratic equation but the answer i got does not look correct.

    Would someone tell me what should i do instead?

    P.S
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  2. #2
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    Quote Originally Posted by Paymemoney View Post
    Hi

    I need help on the following question:

    1) Find the exact values of the x-coordinates of the points of inflection on the graph of y=2x^4+4x^3-x^2+7x-1

    Ok this is what i have done:
    \frac{dy}{dx} = 8x^3 + 12x^2 - 2x +7

    \frac{d^2y}{dx^2} = 24x^2+24x-2

    make \frac{d^2y}{dx^2} = 0

    Now i tried using the quadratic equation but the answer i got does not look correct.

    Would someone tell me what should i do instead?

    P.S

    x = \frac{-3 \pm 2\sqrt{3}}{6}
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  3. #3
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    i get  \frac{-24+\sqrt{768}}{48} and  \frac{-24-\sqrt{768}}{48}?

    which value is the POI??
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  4. #4
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    Quote Originally Posted by Paymemoney View Post
    i get  \frac{-24+\sqrt{768}}{48} and  \frac{-24-\sqrt{768}}{48}?

    which value is the POI??
    both are ... why?
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  5. #5
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    isn't one of the values a minimum?
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  6. #6
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    Quote Originally Posted by Paymemoney View Post
    isn't one of the values a minimum?
    both inflection points are marked in red ...
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  7. #7
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    ok, if i was asked to find the minimum how would i find it??

    Would i take the derivative again?
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  8. #8
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    Quote Originally Posted by Paymemoney View Post
    ok, if i was asked to find the minimum how would i find it??

    Would i take the derivative again?
    minimum will be where the first derivative equals 0 ... you'll need to use a calculator to solve the cubic equation.
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