Question 1

Paper 1Medium6 marks

A model for the water level in a test tank is

h(t)=0.2t3−1.14t2+1.566t+42,h(t)=0.2t^3-1.14t^2+1.566t+42,

where hh is the water level in centimetres and tt is the time in hours after the start of a test. The model is valid for 0≤t≤40\leq t\leq4

(a)

Show that

dhdt=0.6t2−2.28t+1.566.\frac{dh}{dt}=0.6t^2-2.28t+1.566.
[2]
(b)

Hence determine the intervals in the model domain for which dhdt>0\frac{dh}{dt}>0 and dhdt<0\frac{dh}{dt}<0 State when the water level is increasing and when it is decreasing. Give boundary times to 2 decimal places.

[4]

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