IB Math AI Worksheet SL 5.6 - Local Maxima & Minima

This IB Maths AI SL 5.6 – Local Maxima & Minima resource develops students’ understanding of how derivatives are used to identify and classify turning points on curves. Learners focus on critical points, where the derivative is zero or undefined, and use both the first derivative test and second derivative test to determine whether these points represent local maxima or local minima. The material builds clear connections between algebraic derivative information and changes in graphical behaviour.

Structured tasks guide students through differentiating functions, solving (f’(x)=0), and constructing sign charts to interpret where functions increase or decrease. Students learn to recognise how sign changes in the derivative indicate turning points, and how concavity information from the second derivative supports classification. Conceptual prompts emphasise the difference between local and absolute extrema, reinforcing exam-relevant reasoning.