understand the concept of a variable rate of change

differentiate integer powers of $x$

determine gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs

Find the coordinates of the maximum and minimum points

distinguish between maxima and minima by considering the general shape of the graph only

apply calculus to linear kinematics and to other simple practical problems

The displacement, $s$ metres, of a particle from a fixed point $O$ after $t$ seconds is given by:
$s = 24t^2 - t^3, 0 \leq t \leq 20$
Find expressions for the velocity and the acceleration.