Functions with CornersTangent lines don't necessarily exist at every point on a graph. Below there are some examples of functions which have "corners" - sharp turns where tangent lines cannot exist. Recall that one way to think about a tangent line is that if you zoom into the point far enough then the graph eventually looks like a line. Try zooming into the corners and notice that they never go away, i.e. the graph does not resemble a line no matter how far you zoom in.
Jamie Mulholland |