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Applications of Differentiation: Rate of Change, Increasing and Decreasing Functions
Differentiation: Rate of Change Practice 1

 Two variables x and y are related by the equation . Given that
 the variable x is increasing at the rate of 0.1 unit/s, find the rate at which variable
 y changes when x = 2.
 The area of a circular disc increases at a constant rate of 0.05 cm2/s. Find the
 rate at which its radius is increasing when the area is 25 cm2. Give your
 answer correct to 3 significant figures.
 Water is being poured into a container at a rate of 3 cm3/s. The volume, V cm3, of
 the water in the container, when the depth is x cm, is given by
 V = 0.005x3 + 1.2x2. Find
 (a) the rate of increase in the depth of water when x = 5 cm,
 (b) the depth of water when the rate of increase in the depth is 0.15 cm/s.
 Give your answers correct to 2 decimal places.
A circular ink blot starts with a radius of 3 cm. As the ink soaks into the paper, the
blot expands so that after t seconds, the radius, r cm, is given by r = 3 + 0.1t.
(i) Write down an expression for the area, A cm2, of the blot after t seconds.
(ii) Find the rate of increase of the area of the blot that after 4 seconds, leaving
your answer in terms of .