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    Curve C has equation y=e^{2x}+x^2+4x+1

    Show that the x-coordinate of any stationary point of C satisfies the equation. x=-2-e^2x

    I differentiated the equation, then equated it to 0 and got
    2e^{2x}+2x+4=0
    I assume I have to solve for x, but I get stuck at
    e^{2x}+x=\frac{e-4}{2}

    Could anyone help?
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    (Original post by joyoustele)
    Curve C has equation y=e^{2x}+x^2+4x+1

    Show that the x-coordinate of any stationary point of C satisfies the equation. x=-2-e^2x

    I differentiated the equation, then equated it to 0 and got
    2e^{2x}+2x+4=0
    I assume I have to solve for x, but I get stuck at
    e^{2x}+x=\frac{e-4}{2}

    Could anyone help?
    I'm not sure how you ended up with that. You don't need to "solve for x" here, instead just rearrange your equation to get to their one. So you have

    2e^{2x}+2x+4=0

    and you need

    x=-2-e^{2x}

    Start by moving the 2e^{2x} and the 4 to the other side.
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    (Original post by Notnek)
    I'm not sure how you ended up with that. You don't need to "solve for x" here, instead just rearrange your equation to get to their one. So you have

    2e^{2x}+2x+4=0

    and you need

    x=-2-e^{2x}

    Start by moving the 2e^{2x} and the 4 to the other side.
    Oh, I just didnt understand the Question. So if a question was to say show that something x satisfies [equation], do I just always rearrange to make their equation?
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    (Original post by joyoustele)
    Oh, I just didnt understand the Question. So if a question was to say show that something x satisfies [equation], do I just always rearrange to make their equation?
    Yes.

    What else could you do?
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    (Original post by joyoustele)
    Curve C has equation y=e^{2x}+x^2+4x+1

    Show that the x-coordinate of any stationary point of C satisfies the equation. x=-2-e^2x

    I differentiated the equation, then equated it to 0 and got
    2e^{2x}+2x+4=0
    I assume I have to solve for x, but I get stuck at
    e^{2x}+x=\frac{e-4}{2}

    Could anyone help?
    dy/dx= 2e^2x+ 2x+ 2
    at stationary point dy/dx=0 therefore
    2e^2x+2x+4=0
    e^2x+x+2=0
    x= -2-e^2x
    is that right?
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    (Original post by joyoustele)
    Oh, I just didnt understand the Question. So if a question was to say show that something x satisfies [equation], do I just always rearrange to make their equation?
    Isn't that clear from the question? Why would you try to make a different equation instead of the one they give you?
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    (Original post by Notnek)
    Isn't that clear from the question? Why would you try to make a different equation instead of the one they give you?
    Argh nevermind...Im a noob

    Thanks for your help
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    (Original post by etothepiiplusone)
    Yes.

    What else could you do?
    Ermm... Not do what they asked you to do
    Spoiler:
    Show

    Im just kidding...Thanks for your help. You see I'm just a noob
 
 
 
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