Identifying Relative Maxima and Minima on Function Graphs

Miacademy & MiaPrep Learning Channel

This video serves as a clear, introductory guide to identifying relative maxima and minima on function graphs. Hosted by a narrator named Justin, the lesson begins by defining these terms not through rigorous calculus definitions, but through visual intuition: maxima are 'hills' or points higher than their immediate surroundings, while minima are 'valleys' or points lower than their neighbors. The video clarifies the correct plural forms (maxima/minima) and distinguishes between relative extrema and absolute extrema using visual examples. The content progresses through three specific graphical examples, increasing in complexity. First, a simple downward-opening parabola is used to identify a single relative maximum. Next, a cubic-like polynomial curve demonstrates how a point can be a relative maximum even if other parts of the graph are higher, reinforcing the concept of 'local' behavior. Finally, viewers are given a practice opportunity with a W-shaped graph to identify relative maxima and minima on their own, concluding with an introduction to the concept of an absolute minimum. For educators, this video is an excellent resource for Algebra I, Algebra II, or Pre-Calculus courses. It addresses common student misconceptions, such as the belief that a maximum must be the highest point on the entire graph. The visual approach of drawing boxes around specific points to isolate 'neighborhoods' helps scaffold the definition of local extrema before students encounter formal mathematical definitions involving intervals.