91Ó°ÊÓ

. The luminous intensity \(I\) candelas of a lamp at varying voltage \(V\) is given by \(I=4 \times 10^{-4} V^{2}\). Determine the voltage at which the light is increasing at a rate of \(0.6\) candelas per volt.

The distance \(x\) metres moved by a car in a time \(t\) seconds is given by \(x=3 t^{3}-2 t^{2}+4 t-1\). Determine the velocity and acceleration when (a) \(t=0\) and (b) \(t=1.5 \mathrm{~s}\).

The angular displacement \(\theta\) radians of a flywheel varies with time \(t\) seconds and follows the equation \(\theta=9 t^{2}-2 t^{3}\). Determine (a) the angular velocity and acceleration of the flywheel when time, \(t=1 \mathrm{~s}\), and (b) the time when the angular acceleration is zero.

Find the maximum and minimum values of the curve \(y=x^{3}-3 x+5\) by (a) examining the gradient on either side of the turning points, and (b) determining the sign of the second derivative.

Locate the turning point on the following curve and determine whether it is a maximum or minimum point: \(y=4 \theta+\mathrm{e}^{-\theta}\)

. Determine the co-ordinates of the maximum and minimum values of the graph \(y=\frac{x^{3}}{3}-\frac{x^{2}}{2}-6 x+\frac{5}{3}\) and distinguish between them. Sketch the graph.

Determine the height and radius of a. cylinder of volume \(200 \mathrm{~cm}^{3}\) which has the least surface area.

Find the diameter and height of a cylinder of maximum volume which can be cut from a sphere of radius \(12 \mathrm{~cm}\).