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Parallel Tangents to Cubic Graph

  1. Sep 27, 2008 #1
    1. The problem statement, all variables and given/known data
    I have the graph of a function f(x)=(x+1)(x+4)(x+6). I've found the tangent at x=-6, the equation of which is y=10x+60. I then need to algebraically find the equation of another tangent on the curve which is parallel to the first.

    2. Relevant equations
    No idea.

    3. The attempt at a solution
    Since I'm graphing this on Autograph I've managed to find a point where the tangent is parallel to the first, but since this can be done without the computer program I'm really interested to know how it's done. So yeah, I know that the tangent I'm trying to find will have a gradient of 10 but that's about it...

    Any help would be great,
  2. jcsd
  3. Sep 27, 2008 #2


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    Staff Emeritus
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    Homework Helper

    Okay, you know you're looking for a tangent line with a slope of 10.

    Can you write an equation for the slope of the tangent (as a function of x), and set that equal to 10?
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