IB Math AI 5.6 - Local Maxima & Minima Notes

This IB Maths AI SL 5.6 – Local Maxima & Minima (Student Notes) resource develops students’ understanding of stationary points and the first derivative test in a clear, structured way. The notes guide learners through the key idea that turning points occur where the gradient is zero, helping them connect algebraic differentiation with graphical interpretation. Students are introduced to the concept of stationary points by setting the derivative equal to zero and solving to find critical values of ( x ) .

A fully worked example walks students step-by-step through differentiating a quadratic function, solving ( f’(x)=0 ), finding the corresponding ( y )-value, and using sign changes in ( f’(x) ) to classify the point as a local maximum or minimum . The first derivative test is clearly explained, with emphasis on how changes from positive to negative gradients indicate a local maximum, while changes from negative to positive indicate a local minimum. Visual graphs reinforce conceptual understanding by showing how the algebra connects directly to the curve’s turning points.

(Note: The student + teacher notes are free! Thanks for your support. Consider purchasing the IB Math AI 5.6 – Local Maxima & Minima PPT to supplement these. Feel free to share this link, and don’t forget to leave a 5-star review if you found these helpful.)