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Math Help - Check my work?

  1. #1
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    Check my work?

    Here's the problem:

    "Find the x-coordinate of all points on the graph of f(x)=-2x^3+2x+1 where the tangent line is parallel to the line y=-7x+2."

    I took the derivative of f(x) and got f'(x)=-6x^2+2. Then I set the slope of the line y equal to this equation, so as to have -7=-6x^2+2. So I solved for x and got x^2=-(9/6) and so x=1.225 (after taking the square root).

    I went ahead and found the actual tangent line of this by plugging that x-value back into the derivative of f(x), ending with y=-7(x+1.225)+7.

    I'm pretty sure I did the process right, but if I didn't, could someone kindly correct me? Or tell me if I'm leaving something out? I feel like there's something else that should be done.
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  2. #2
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    Quote Originally Posted by Rumor View Post
    Here's the problem:

    "Find the x-coordinate of all points on the graph of f(x)=-2x^3+2x+1 where the tangent line is parallel to the line y=-7x+2."

    I took the derivative of f(x) and got f'(x)=-6x^2+2. Then I set the slope of the line y equal to this equation, so as to have -7=-6x^2+2. So I solved for x and got x^2=-(9/6) and so x=1.225 (after taking the square root).

    I went ahead and found the actual tangent line of this by plugging that x-value back into the derivative of f(x), ending with y=-7(x+1.225)+7.

    I'm pretty sure I did the process right, but if I didn't, could someone kindly correct me? Or tell me if I'm leaving something out? I feel like there's something else that should be done.

    f'(x)=-6x^2+2=-7

    So

    -6x^2=-9

    x^2=\frac{9}{6}

    Now you need both positive and negative square root
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  3. #3
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    Quote Originally Posted by Rumor View Post
    Here's the problem:

    "Find the x-coordinate of all points on the graph of f(x)=-2x^3+2x+1 where the tangent line is parallel to the line y=-7x+2."

    I took the derivative of f(x) and got f'(x)=-6x^2+2. Then I set the slope of the line y equal to this equation, so as to have -7=-6x^2+2. So I solved for x and got x^2=-(9/6) {-9/6 ???} and so x=1.225 (after taking the square root).

    I went ahead and found the actual tangent line of this by plugging that x-value back into the derivative of f(x), ending with y=-7(x+1.225)+7.

    I'm pretty sure I did the process right, but if I didn't, could someone kindly correct me? Or tell me if I'm leaving something out? I feel like there's something else that should be done.
    -6x^2+2 = -7

    x^2 = \frac{3}{2}

    x = \pm \sqrt{\frac{3}{2}}

    you forgot the negative solution for x.
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  4. #4
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    Oh, of course! I knew there was something.. Thanks to the both of you. :]
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