# Derivatives and the Shape of a Graph - An absolute extremum of a function over a given interval is a maximum or minimum of the function over the interval. - An absolute extremum of a function over a given interval may occur at an endpoint of the interval. - An absolute extremum is a y-value. - The location of an absolute extremum is an x-value. > [!NOTE] Critical Points > To find critical points, we need to find the values of the variable that make the derivative either 0 or undefined. ## Maxima and Minima https://openstax.org/books/calculus-volume-1/pages/4-3-maxima-and-minima ## The First Derivative Test ![[Pasted image 20240923024802.png|439]] ## The Second Derivative Test