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In this chapter we look at how it is possible to describe relationships which are changing and how we can find out the rate of this change.
The chapter is split up into the following sections.
8.A Some problems answered and difficulties solved
(a) How can we find a speed from knowing the distance travelled?
(b) How does y = xn change as x changes?
(c) Different ways of writing differentiation: dx/dt, f’(t), , etc.,
(d) Some special cases of y = axn,
(e) Differentiating x = cos t answers another thinking point,
(f) Can we always differentiate? If not, why not?
8.B Natural growth and decay – the number e
(a) Even more money – compound ...