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4.05 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(11t)3, for $0\le t\le11$0t11.

a

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.

b

At what rate is the volume of water in the pool changing after $10$10 minutes?

c

Select the time $t$t at which the pool is emptying at the fastest rate.

$t=11$t=11 mins

A

$t=5$t=5 mins

B

$t=0$t=0 mins

C

$t=10$t=10 mins

D
Easy
7min

The height in metres of a projectile above flat ground is given by $h=9+8t-t^2$h=9+8tt2, where $t$t is given in seconds.

Medium
2min

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=16t4t2 where $t$t is given in seconds.

Easy
1min
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Outcomes

MA12-3

applies calculus techniques to model and solve problems

MA12-6

applies appropriate differentiation methods to solve problems

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