A particle moves along a line with position $s (t) = t^{3} - 6 t^{2} + 9 t$ . At what times is the particle at rest?

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What is the derivative of $f (x) = ln (x^{2} + 4)$ ?
What is the equation of the tangent line to $f (x) = x^{3} - 3 x + 2$ at the point where $x = 2$ ?
At which critical point does $f (x) = x^{3} - 12 x$ attain a local minimum?
On which interval is the function $f (x) = x e^{- x}$ strictly increasing?
Rolle's theorem applied to $f (x) = x^{2} - 4 x + 3$ on the interval $[1, 3]$ guarantees a point $c$ where $f^{'} (c) = 0$ . What is $c$ ?
Where is the inflection point of the cubic polynomial $f (x) = x^{3} - 6 x^{2} + 9 x + 1$ located?

A particle moves along a… | Panhellenic Examinations (Greece)