At rest, the human heart beats once every second. At the strongest part of the beat, a person’s…

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.]

• Note: There are penalties for late assignments. You must contact your tutor

before the due date if you have difficulties making the deadline

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