Re:The Calculus They Won't Teach You [video]
by dvt on Wednesday January 04, 2023 @04:47PM
(#34252284)
> problems to solve like "find the maximum" and "find the relationship between these two variables"
I think these are actually pretty abstract, so it's hard exactly to grasp what a derivative is until maybe Calc II or III -- imo, the main problem is that it just seems like mathematical black magic: you need to define a limit, you need to use that definition to subtract two slopes, the complexity of which magically kind of vanishes, and you end up with a "method" for spitting out derivatives. Whereas finding area under a curve seems like a common sense thing to do: you take smaller and smaller slices of a thing and add it all up.
I do agree that if you really learn anti-derivatives (which, by all accounts, is harder), you basically get derivatives for free.
I think these are actually pretty abstract, so it's hard exactly to grasp what a derivative is until maybe Calc II or III -- imo, the main problem is that it just seems like mathematical black magic: you need to define a limit, you need to use that definition to subtract two slopes, the complexity of which magically kind of vanishes, and you end up with a "method" for spitting out derivatives. Whereas finding area under a curve seems like a common sense thing to do: you take smaller and smaller slices of a thing and add it all up.
I do agree that if you really learn anti-derivatives (which, by all accounts, is harder), you basically get derivatives for free.