When i was at school i used to think that any line that touches a curve at only one point is called as the tangent at that point to the curve! But after reading derivative i think this definition of tangent is not correct at all conditions! For example, x-axis cannot be called as tangent at origin to the function y=|x| though it touches the curve at origin only! second example, tangent at a point on a curve y=sin x may also touch any other point on the same curve(thus there are two points of intersection) IS this new concept of tangent i have is right OR the definition of tangent at school is right? please help!