1. Differentiate the following functions with respect to x.
(a) Use the quotient rule to differentiate
(b) Use the Chain rule to differentiate
(c) Select an appropriate rule to differentiate
2. The angular displacement, θ radians, of the spoke of a wheel is given by
the expression θ = 0.5t4 – t3, where t is time in seconds. Find:
(a) The angular velocity after 2 seconds.
(b) The angular acceleration after 3 seconds.
(c) The time when the angular acceleration is zero.
3. From a rectangular sheet of metal measuring 120 mm by 75mm, equal
squares of side x are cut from each of the four corners. The remaining
flaps are then folded upwards to form an open box.
(a) Draw a neat and simple diagram of the rectangular sheet of metal
(not drawn to scale) and show the dimensions given including the
squares of side x.
(b) Show that the volume of the box is given by:
(c) Find the value of x such that the volume is a maximum.