A vertical tangent line is a line that is perpendicular to the curve of a function at a specific point and has an undefined slope. It occurs when there is an abrupt change in direction or when the slope becomes infinite.
Absolute value functions can also have vertical tangent lines at certain points where they abruptly change direction, similar to other types of functions.
A discontinuity is a point where a function is not continuous, meaning there's a break or jump in the graph. It's like encountering a pothole on the road - you have to slow down or change direction.
The derivative of a function represents its rate of change at any given point. When the derivative is undefined at a specific point, it indicates the presence of a vertical tangent line.