IB Math AI Worksheet SL 5.2 - Increasing & Decreasing Functions

This IB Maths AI SL 5.2 – Increasing & Decreasing Functions resource strengthens students’ understanding of how derivatives describe the behaviour of functions across intervals. Learners use the sign of the derivative to determine where a function is increasing, decreasing, or constant, reinforcing the interpretation of the derivative as slope and linking algebraic information directly to graphical movement. The material develops fluency in describing function behaviour using precise calculus language and interval notation.

Structured tasks guide students from core definitions to practical application. Sign charts are used to connect derivative signs with local maxima, local minima, and stationary points, while worked examples model how to differentiate, solve f′(x)=0, and test intervals. Interpretation questions require students to move between derivative conditions and graph sketches, deepening conceptual understanding of how calculus describes overall function shape.