1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    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


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook