A bounded derivative refers to a derivative of a function that is limited in magnitude, meaning there exists a constant $M$ such that for all points in its domain, the absolute value of the derivative is less than or equal to $M$. This concept is important when comparing functions and understanding their continuity properties, especially in relation to pointwise continuity, where boundedness of the derivative can imply certain behaviors about the function's smoothness and growth.
congrats on reading the definition of bounded derivative. now let's actually learn it.