Aiming at the pain points in the teaching of "Monotonicity and Extrema of Functions" in Applied Advanced Mathematics

such as "difficulty in understanding abstract concepts

difficulty in breaking through key and difficult points

and low student participation"

this paper proposes an integrated teaching model of "Artificial Intelligence + Traditional Culture". Taking GeoGebra software as the core AI tool

it visually demonstrates the correlation between the positive/negative nature of derivatives and the monotonicity of functions; and integrates the poetic artistic conception of Su Shi's "Inscription on the Wall of West Forest Temple" and the image of Lushan Mountain's terrain to materialize the abstract concept of extrema. Each peak

though not necessarily the highest across the entire range

stands as the local maximum in its vicinity; similarly

each valley

while not the lowest overall

serves as the local minimum nearby.This paper constructs a teaching closed loop of "artistic conception introduction—visual exploration—precision breakthrough—personalized consolidation". Practice shows that this model can effectively reduce students' cognitive load

improve classroom interaction and teaching effect

and provide a replicable teaching reform plan for Applied Advanced Mathematics teachers.