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Anonymous
Definition of derivative? 2016-07-27 22:39:01 Post No. 162951
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Definition of derivative? 2016-07-27 22:39:01 Post No. 162951
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Hey, I'm at a high school student and at past lessons we learned that the definition of the derivative is
f'(x) = lim(Δx->0) [f(x+Δx)-f(x)]/Δx
But I never actually understood what this really means. I know that it is the rate of which a slope changes, but I don't get how this formula describes that. Maybe I'm just dumb but I need help
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>>162951
Let's say you have two points on a curve. You can get the slope of the line create by those two points by using the slope formula: [f(x2) - f(x1)]/x2 - x1. Now say that we want the slope of the curve from one specific point. What we do is take the desired point and a point right in front of it and apply the slope formula to give us a really close approximation of what that slope would be. We can represent that with: [f(x+Δx)-f(x)]/Δx If you think about it, the closer the two chose points are to each other, the more accurate the result would be. Therefore, it we take the limit as the distance (Δx) approaches 0, we get an accurate reading of what the slope would be at single point, AKA the derivative.
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>>162951
>>162968
Here's a good visual.
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https://www.youtube.com/watch?feature=player_detailpage&v=ANyVpMS3HL4#t=430
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underage ban
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thanks for all the help
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