At rest, the human heart beats once every second. At the strongest
part of the beat, a person’s blood pressure peaks at 120mmHg. At the most
relaxed part of the beat, a person’s blood pressure drops to 80mmHg. Supposing
that t = 0 corresponds to the peak of the beat, write down a trigonometric
function that captures this behaviour. Sketch the blood pressure over two heart
beats.
3. [8 marks] The volume of grains in a silo at a particular time (measured in hours)
is given by V (t) = 4t(3-t) m3
. Find the rate of change of the volume of grains
in the silo from first principles (using the definition of the rate of change).
4. [12 marks] Consider the function f(x) = 2x
2 + 1. Find the equation of the
tangent to the graph of f(x) at x = 2. [NOTE: when calculating f
0
(2), use first
principles.]
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