Learning Resources

Investigation 8: The Derivative

Some of you may instinctively write that a tangent is a line that touches a curve in exactly one point, or touches a curve but does not cross it. However, in your definition, it is important to mention that a tangent line can be created such that it touches the curve in more that one place. As well, it is possible for the tangent line to cross the curve at the point of tangency. The graphs below illustrate each of the fore mentioned cases. These scenarios create the need for a more precise definition of a tangent.