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Math Help - Tangent to the curve

  1. #1
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    Tangent to the curve

    Here's the question:

    There are two points on the curve y = x^4 - 2x^2 - x that have a common tangent line. Find those points.

    I'm stuck.

    (ps. sorry for double post but the previous one had a poor title)
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by finch41 View Post
    Here's the question:

    There are two points on the curve y = x^4 - 2x^2 - x that have a common tangent line. Find those points.

    I'm stuck.

    (ps. sorry for double post but the previous one had a poor title)
    f'(x)=4x^3-4x-1

    So we have that y-f(x_0)=f'(x_0)(x-x_0)
    so then we would have y-(x_0^4-2(x_0)^2-x_0)=(4x_0^3-4x_0-1)(x-x_0)
    Can you see what to do from there?
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  3. #3
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    i think i did that but i cannot figure out what to do with it... since it will have two variables x and x1
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  4. #4
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    so like no one can do this?

    i gave it to my math teacher today and he tried some stuff and dediced best to take it home and look at it later
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  5. #5
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    solved... or is it?

    well see i got the answer
    i decided i would sketch the curve accurately so i found all the important points and then estimated the common tangent

    and along the process i found that f prime of 1 and f prime of -1 are both -1
    and when i finished sketching the curve i estimated the common tangent line at about those points

    and when i found the equation of the tangent line at each point they turn up the same equation

    but is this luck?

    is there a more methodical approach?

    hmm...
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