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Graph question

  • Thread starter Mejiera
  • Start date
  • #1
15
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Homework Statement



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

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #3
18
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Simply put, if you can differentiate it, it has tangent lines. So you can have tangent lines for things that aren't functions too.
 
  • #4
15
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but the tangent line touches a cubed function twice so im sure if it could really be called a tangent line
 
  • #5
33,181
4,860
but the tangent line touches a cubed function twice so im sure if it could really be called a tangent line
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.
 
  • #6
jbunniii
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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.
 
  • #7
15
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ok thanks for clearing that up guys.
 

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