11.11 Optimisation problems
Interactive practice questions
A pool is being emptied, and the volume of water $V$V litres left in the pool after $t$t minutes is given by the equation $V=1500\left(11-t\right)^3$V=1500(11−t)3, for $0\le t\le11$0≤t≤11.
Find the rate of change of the volume after $t$t minutes, $V'\left(t\right)$V′(t).
Enter each line of working as an equation.
At what rate is the volume of water in the pool changing after $10$10 minutes?
Select the time $t$t at which the pool is emptying at the fastest rate.
$t=11$t=11 mins
$t=5$t=5 mins
$t=0$t=0 mins
$t=10$t=10 mins
The height in metres of a projectile above flat ground is given by $h=9+8t-t^2$h=9+8t−t2, where $t$t is given in seconds.
A boy stands on the edge of a sea-cliff with a height of $48$48 m. He throws a stone off the cliff so that its vertical height above the cliff is given by $h=16t-4t^2$h=16t−4t2 where $t$t is given in seconds.