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Homework Help: Graph question

  1. Mar 15, 2010 #1
    1. The problem statement, all variables and given/known data

    is it possible to have a tangent line in a cubed function

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 15, 2010 #2
  4. Mar 15, 2010 #3
    Simply put, if you can differentiate it, it has tangent lines. So you can have tangent lines for things that aren't functions too.
     
  5. Mar 15, 2010 #4
    but the tangent line touches a cubed function twice so im sure if it could really be called a tangent line
     
  6. Mar 15, 2010 #5

    Mark44

    Staff: Mentor

    Doesn't matter. The tangent line is just a line that touches a curve at a point (a, f(a)) and whose slope is f'(a). The fact that the tangent line happens to intersect the graph of the function somewhere else is immaterial. Pretty much every odd-degree polynomial will have a tangent line that intersectst the curve somewhere else.

    As it turns out, the tangent line to the graph of y = f(x) = 2x + 3 at any point happens to completely coincide with the graph of this function, but that doesn't keep it from being a tangent line.
     
  7. Mar 15, 2010 #6

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In addition to what Mark44 said, I will point out that the tangent line can even intersect/cross the curve AT the point of tangency. For example, the tangent to [itex]f(x) = x^3[/itex] at [itex]x = 0[/itex]. It's still a tangent line, though.
     
  8. Mar 15, 2010 #7
    ok thanks for clearing that up guys.
     
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