At x=2, y is x^2 , which is 4. at x=3, y is 9. If y is changing at a rate of 2x for every change in x, wouldn’t that make y at x=3 6, because you moved 1 along the x so you move 2 along y? Or how does this work? I’m having trouble understanding differentiation 🙁
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The issue is that, since the slope is 2x, it changes as you change x. At x = 1, the slope is 2; at x = 1.0000000001, the slope is 2.0000000002; and so on for any tiny changes in x.
If you wanted to calculate what the position was using the slope, you’d have to calculate it at a high precision, and to do it iteratively (use slope = 2 to find y at x = 1.00000001, recalculate the slope, then use it to find y at x = 1.00000002, and so on). You can’t easily do the math out algebraically for this; this is why calculus was invented, to deal with these situations.
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