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Derivatives have nice physical problems to solve like "find the maximum" and "find the relationship between these two variables" which you can find by measuring
by 8note 4y ago
Derivatives have nice physical problems to solve like "find the maximum" and "find the relationship between these two variables" which you can find by measuring a linear slope a lot of times. Learning derivatives starts with linear regression, which you do when learning about lines on a Cartesian plane.
By the time you know about drawing lines on planes to find the integral area underneath, you've already figured out the derivative so you know what direction to move your pen in next while drawing the line
- dvt 4y ago> 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.