1.7.14 Stationary points

The altitude $h$ (in meters) of a specialized research drone during a 10-second test flight is modeled by the function

h(t) = t^3 - kt^2 + 15t - 12

where $t\,$ is the time in seconds ( $\le t \le 10$ ) and $k\,$ is a constant.

Find, in simplest form, (i) $h^{'} (t)$ (ii) $h^{''} (t)$

[2]

The curve with equation $v = h^{'} (t)$ (velocity) intersects the curve with equation $a = h^{''} (t)$ (acceleration) at the points $P\,$ and $Q$ .

Given that the $t$ -coordinate of $P\,$ is 5,

find the value of $k$ .

[2]

Hence find the coordinates of $Q$ .

[4]

1.7.14 Stationary points Questions