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Struggling with how calculus and integration actually look on a graph? In this video, we break down a 2024 Leaving Cert Higher Level Paper 1 question (Q6b). We focus on understanding the relationship between a function, its derivative, and the definite integral without getting bogged down in complex numbers. We cover: How to identify where the derivative is negative by looking at the slope. Understanding definite integrals as the "area under the curve." Determining the range of values where an integral remains positive by comparing areas above and below the x-axis. Perfect for Irish secondary school students preparing for the Leaving Cert Maths exam! 0:00 Introduction to the function graph 0:22 Defining the function f(x) and its domain 0:55 Finding where the derivative f'(x) is negative 1:28 Explaining the link between derivative and slope 2:06 Moving on to integration and areas 2:35 Finding the range of values for a positive integral 3:13 Comparing areas above and below the x-axis 4:18 Final summary of the range of a Leaving Cert Maths, Higher Level Maths Ireland, LC Maths Paper 1, Calculus Graphs, Integration Explained, Area Under a Curve, Maths School of Grinds, Irish Education, Leaving Cert 2024, Secondary School Maths, Maths Made Easy, Calculus Revision