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Q7. (a) The displacement, s metres, of a body from a fixed point is given by the equation:

s = 48t + 8t² - 4/3 t³, where t is the time in seconds.

Determine EACH of the following for the body:

(i) the time (t > 0) when its velocity is zero. (5)

(ii) the time when its acceleration is zero. (2)

(iii) its acceleration after FIVE seconds. (1)

(b) Given P = 3cos x - 1/√x + In x³, determine dP/dx and (d² P)/dx² .(8)