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Math Help - Derivative HELP!!

  1. #1
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    Derivative HELP!!

    show that the curve y=6x3+5x-3 has no tangent line with slope 4.

    please help me show how i prove this!!!!
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Derivative HELP!!

    Take the derivative, equate to 4, and what do you find?
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    Re: Derivative HELP!!

    if you do y'(4) it equals 293 so is that the proof?
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Derivative HELP!!

    No, you aren't being asked to evaluate y'(4), you are being asked to show that there is no real x such that:

    y'(x)=4.
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  5. #5
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    Re: Derivative HELP!!

    so how do you do that? whats the difference?
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Derivative HELP!!

    First, take the derivative of y with respect to x, then set that equal to 4 and solve for x. What do you find?

    edit: I realize this is the same thing I said in my first post, but to say any more would be to essentailly give away the problem, and this would do you little good.
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  7. #7
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    Re: Derivative HELP!!

    well if you take the derivative and set it equal to 4 and solve you get plus or minus sqrt(-1/18) which is a nonreal answer so is that why there is no tangent line with the slope 4?
    Quote Originally Posted by MarkFL2 View Post
    First, take the derivative of y with respect to x, then set that equal to 4 and solve for x. What do you find?

    edit: I realize this is the same thing I said in my first post, but to say any more would be to essentailly give away the problem, and this would do you little good.
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: Derivative HELP!!

    Yes, you've hit the nail on the head!
    Thanks from pnfuller
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