IB Math AI 5.2 - Increasing/Decreasing Functions Notes

This IB Maths AI SL 5.2 – Increasing & Decreasing Functions resource develops students’ understanding of how derivatives describe the behaviour of functions. Learners connect the sign of the derivative to whether a function is increasing, decreasing, or constant, building intuitive links between gradient, slope direction, and graphical movement from left to right. The material reinforces the key idea that the derivative represents the slope of the curve at a point, allowing students to interpret function behaviour directly from calculus notation.

Structured notes and guided explanations lead students through defining increasing, decreasing, and constant intervals using derivative conditions. Visual reasoning prompts help learners justify why a positive slope corresponds to growth, a negative slope to decline, and a zero slope to flat (constant) behaviour. Sign summaries and derivative-based reasoning tasks strengthen conceptual understanding before formal practice.

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