Functions and Calculus is one of the strands of the new Project Maths Course in the Irish curriculum. Functions provides an essential link between Algebra and Number and introduces the students to applications of calculus in the real world. Use of differentiation to find the slope of a tangent to a curve at a specified point is introduced. This is then extended to the study of increasing and decreasing functions. Functions and Differentiation are used in real life to help us understand rates of increase and decrease. For example, students will solve problems involving the maximum speed reached by a car and the highest point reached by a firework or rocket. Finally, the concept of numerical integration is introduced through the use of the ‘Trapezoidal Rule’ to find areas under specific curves. It is an interesting topic that is very accessible to all students.
Having completed this course students will be able to:
- Basic Differentiation of functions;
- The rules of differentiation (product rule, quotient rule, chain rule);
- Determine the local maxima and local minima turning points of a curve;
- Understand rate of change of distance;
- Use slope to determine the nature of a function;
- How to use the Trapezoidal Rule to find area.
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