Applications of derivatives

Derivatives model real change: if s(t) = t^3 - 6t^2 + 9t gives an object's position, its velocity is v(t) = 3t^2 - 12t + 9. Setting v(t) = 0 gives 3(t-1)(t-3) = 0, so the object is momentarily at rest at t = 1 and t = 3. These are critical points, also used to find a function's maximum or minimum values.

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