Use the quotient rule, 𝑑(𝑢 𝑣) 𝑑𝑥 = 𝑣𝑑𝑢 𝑑𝑥−𝑢𝑑𝑣 𝑑𝑥 𝑣2, to determine the derivative of quotients of functions involving power and polynomial functions.

Find $\frac{d}{dx}\left(\frac{3x^2 + 2}{x^3 - 1}\right)$.

A particle moves along a straight line. Its velocity \( v \) metres per second at time \( t \) seconds is given by \[ v(t) = \frac{3t^2 + 5t - 2}{2t + 1} \] where \( t \geq 0 \). **(a)** Use the quotient rule to find an expression for the acceleration \( a(t) \) of the particle at time \( t \). [3 marks] **(b)** Hence, determine the acceleration of the particle when \( t = 2 \), giving your answer correct to two decimal places. [1 mark] **(c)** Use your result from part (a) to find the time \( t \) when the acceleration of the particle is zero. [1 mark]