The speed of the car, given by \(v(t)=-6t^2+12t+60~\text{km/h}\).

i) How fast was the car travelling initially?
ii) When did the car reach its maximum speed?

A manufacturer finds the profit \(\$P\) from making \(x\) woggles per day is given by \(P=-x^2+50x-200\). 

i) If no woggles are made, what is the loss?
ii) What is the maximum profit?

The temperature \(T^\circ\) in a town \(t\) hours after 8 pm is given by:\[T=\dfrac{1}{4}t^2-4t+10\]

i) At what time is the temperature a minimum?
ii) What is the minimum temperature?

The height of a ball \(t\) seconds after it is thrown into the air is given by: \(h(t)=9+16t-4t^2\)

i) What is the maximum height reached by the ball?

ii) How long will it take for the ball to fall back to the ground?

The profit in manufacturing washing machines per day is given by \(P=-3x^2+240x-400\) dollars.

i) How many washing machines should be made each day to maximise profit?

ii) What is the maximum profit? 

The graph of \(y=x^2-5x\) and \(y=-x^2+3x\) are illustrated. 

Find the maximum vertical separation between the two curves for \(0 \le x \le 4\)

The height of a rocket \(t\) seconds after it is fired vertically upwards is given by \(h(t)=80t-5t^2\)

i) How long does it take for the rocket to reach its maximum height?

ii) Find the maximum height reached by the rocket. 

The temperature \(\text{T}^\circ \text{C}\) in a country town after 10pm is given by \(T(t)=\dfrac{1}{2}t^2-8t+24\).

i) At what time is the temperature a minimum?

ii) Find the minimum temperature.