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The fastest rate of change is at the point where the sine wave crosses the axis, where the value of the sinewave is zero and the slowest rate of change is at the top (and bottom) of the sinewave, where the sinewave reverses direction, which makes the rate of change zero.

At the zero crossing point the rate of change is

(frequency of sinewave) * (amplitude of sinewave) * pi

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Q: Where on a sine wave is the fastest and slowest rate of change?
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