Logging off…
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Well, at least I uh… HAVE A SMILEY FACE AS MY PFP
ha
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THE BIG F IS USED IN MUSIC FOR FORTE AAAASIDIJSRBRIDIDUCSUDUDJW NC HDD DS LEKFKSLAJGUifo i is t pxk is uzu f I C
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MUSIC? MUSIC? I FIRST THAT IS NOT WHAT AUO IS ABOUT. WE WERE TALKING ABOUT MATH.
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You’ve just summed up my pet peeve very well sir
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why is one of the integrals sideways?
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All in a days work, ma’am. Tips Beanine to giant lightning dragon
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Logging off(for real this time though)
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Also why is everyone changing their names is it a new GimTrend?
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Just explain what integrals and derivatives are this is what I understood:
x → a f x-a (big f + 4)
Basically when a person explains it it’s better than Wikipedia or videos.
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Okay, tomorrow I’ll do my best.
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Why has this post turned into calculus lol
Not that I’m complaining ofc
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why are we even calling this big f, that has to be a little f
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I know that when you said secant line you meant two points in a parabola, but wouldn’t the average rate of change for the whole parabola just be 0?
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Parabolas extend beyond bounds, so you can only take the slope of the secant line on an interval.
zypheir time 
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And if both points have the same y-value, then the average rate of change is zero. Makes sense.
To find the instantaneous rate of change, we can use limits. We may not be able to find the rate of change using one point, but we can do something else.
Let’s say Δx is an infinitesimally small number. It can be as small as it needs. For this guide’s sake, Δx can be 0.01.
Normally, average rate of change is in the form
Average Rate of Change = (f(b) - f(a))/b - a, where a and b are the starting and ending points on an interval, respectively.
We can approximate instantaneous rate of change by using an extremely small value plus the starting point of the interval, like [3, 3 + 0.01] to approximate average rate of change.
Now, when we take the limit so Δx (an extremely small value) approaches 0, and the average rate of change becomes this: (f(x + Δx) - f(x))/(x + Δx - x). This is the formal definition of a derivative.
Think about it like this: The smaller Δx becomes, the more accurate our approximation becomes. If we had Δx as 0.0000000000001, then the change in x would become small enough to represent as instantaneous rate of change.