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Math Help - tangent to the function #1

  1. #1
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    tangent to the function #1

    show that there are two tangents to the curve y=(1/5)x^5 - 10x that have a slope of 6.

    So what I did so far is found the derivative of the function which is:

    y'=x^4-10

    Now.. I have the slope in general, but I need to show that there are two tangents with the slope of 6.

    If I did this.. I am just guessing but:

    6=x^4-10
    solve for x and I get x=2 or x=-2 But Still not sure on this..

    Can someone verify/correct me and continue on to finish this? Thanks in advance.
    Last edited by mr fantastic; August 12th 2009 at 05:06 PM. Reason: Changed post title
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by skeske1234 View Post
    show that there are two tangents to the curve y=(1/5)x^5 - 10x that have a slope of 6.

    So what I did so far is found the derivative of the function which is:

    y'=x^4-10

    Now.. I have the slope in general, but I need to show that there are two tangents with the slope of 6.

    If I did this.. I am just guessing but:

    6=x^4-10
    solve for x and I get x=2 or x=-2 But Still not sure on this..

    Can someone verify/correct me and continue on to finish this? Thanks in advance.
    it is correct you have two tangent line have the slope 6 tangent at the point x=2 and tangent at x=-2
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