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
Optimisation Problems
Part 1:
This video explains how to set up equations to ‘optimise’ for maximum volume.
Part 2:
This video explains using the derivative to find possible turning points
Part 3:
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!
