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FactChecker

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First you should consider how the shape of the cup effects the rate of height increase and the derivative of that. I think that your statement in the original post about the first derivative of height increase being positive is not always true as the cup fills up.

Consider the derivatives where the cup diameter is expanding, where it is contracting, the sudden change in the middle, and the constant curvature of the top and bottom halves."

hey factchecker. even if the height derivative fluctuates at the shape of the glass (I know itll slow down drastically at the wide parts, and increase in height quicker at skinnier parts of the cup) wouldn't it still be a positive derivative? i guess i'm trying to imagine this on a graph. I've attached the graph. lets say that at the skinny parts of the cup, it increase 10cm/s. and then at the widest parts of the cup, it decreases to an increase of 4cm/s. isn't it still positive because it's still an increase? or am i just not understanding

thankyou in advance for all your help =)

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# Second derivatives when pouring juice into a cup

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