This is part of the HSC Mathematics Advanced course under the topic of Calculus: Applications of Differentiation. In this post, we solve optimisation problems for any of the functions covered in the scope of this syllabus, in a wide variety of contexts including displacement, velocity, acceleration, area, volume, business, finance, and growth and decay.
- Define variables and construct functions to represent the relationships between variables related to contexts involving optimisation, sketching diagrams or completing diagrams if necessary
- Use calculus to establish the location of local and global maxima and minima, including checking endpoints of an interval if required
- Evaluate solutions and their reasonableness given the constraints of the domain and formulate appropriate conclusions to optimisation problems
This video explains how to set up equations to ‘optimise’ for maximum volume.
This video explains using the derivative to find possible turning points
This video will highlight how to find the hidden conditions and ultimately solve the problem.
Want to learn more? Check out more of our HSC Advanced Maths resources here!