URGENT!! Maths HL IA idea optimization

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Hii

My IA idea submission is due tomorrow and I have no idea what I really want to do, but came up with the idea of optimization using differential equations. I thought of reducing the surface area of packaging in different shapes like sphere and prisms, and calculate the minimum point (minima) through second order differentiation equation. I am also planning to then apply this to different real life examples like Toblerone triangle prism or something like that.

Do you think this is too simple at the level of maths HL because it is just at the level of maths HL in the syllabus? I am ready to discard the idea if the maths involved is too easy for HL. Thanks xx

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I am a bit confused by what specific 2nd order ODE you are talking about. I thought at first you could be thinking to optimize a function that takes in two values eg f(x) = x(x + w)(x - 2w) where you need to consider both x and w to maximize f, but this is not ODE. optimizing (smooth) f: R² --> R functions is interesting on its own.

ODE does not often come directly out out of an optimization problem. ODE is more often used either in a force balance (eg Navier-Stokes), or population growths.

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