Given that y = (3x + 2)⁴(x² - 1),
(a) Find dy/dx, simplifying your answer as far as possible.
(b) Hence, find the values of x for which dy/dx = 0.
(c) A particle moves along a straight line such that its displacement s metres from a fixed point O at time t seconds is given by s = t³ - 3t² - 9t + 5, t ≥ 0.
(i) Find the velocity of the particle at t = 4 seconds.
(ii) Find the acceleration of the particle at t = 2 seconds.
(iii) Determine the time(s) at which the particle is momentarily at rest.

Question

Given that y = (3x + 2)⁴(x² - 1),
(a) Find dy/dx, simplifying your answer as far as possible.
(b) Hence, find the values of x for which dy/dx = 0.
(c) A particle moves along a straight line such that its displacement s metres from a fixed point O at time t seconds is given by s = t³ - 3t² - 9t + 5, t ≥ 0.
    (i) Find the velocity of the particle at t = 4 seconds.
    (ii) Find the acceleration of the particle at t = 2 seconds.
    (iii) Determine the time(s) at which the particle is momentarily at rest.

Accepted Answer

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Answer

A) null

Answer

B) null

Answer

C) null

Answer

D) null

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