|f'(t)|_{\text{max}} = A\omega

February 22, 2026

$|f'(t)|_{\text{max}} = A\omega$

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The rate of change of $ f(t) $ is given by its derivative:
f'(t) = -A\omega \sin(\omega t + \phi)
The maximum rate of change occurs when $ \sin(\omega t + \phi) = \pm 1 $, so:
However, the problem states that the maximum rate of change is $ 5A\omega $, which suggests the given value corresponds to the amplitude of the derivative, i.e.,
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