Critical points

This document is designed for students from Grade 11 to Grade 12 (or equivalent high school levels) studying under international curricula such as GCSE, IGCSE, A-Level, and similar advanced mathematics programs. It is also suitable for learners under various examination boards including Cambridge (CAIE), Edexcel, and other national education systems where calculus and functions are part of the syllabus. The material follows a modern, exam-focused approach that aligns with competency-based learning, helping students build strong conceptual understanding as well as problem-solving skills. Each topic on critical points is explained step by step with clear reasoning, making it highly useful for board exams, school assessments, and entry test preparation where analytical thinking and graph interpretation are require