A function is not differentiable at a certain point if it does not have a derivative at that specific point. This means that the slope of the tangent line cannot be determined at that particular point.
The tangent line to a curve at a certain point is the line that best approximates the behavior of the curve near that point. It shares both location and slope with the curve at that specific point.
A critical point of a function occurs where its derivative equals zero or is undefined. It plays an important role in determining the behavior of the function.