The tangent line is defined to exist if it is the same when the point is approached from both sides.Originally Posted by bobby77
Specifically look at point B. As we approach it from the left side, the tangent line has a negative slope. As we approach it from the right side, the tangent line has a positive slope. Since these two slopes don't agree, there is no tangent line at point B.
Check for yourself to make sure you can apply this argument to see why points A, C, and D have tangents at those points.