Learning objectives
Show that an equation f(x) = 0 has a root between two given values by a change of sign of a continuous function, and use a sketch of two graphs to count the roots
Rearrange an equation into the form x = F(x), and show that if the iteration xₙ₊₁ = F(xₙ) converges then its limit is a root of the original equation
Use a given iteration from a starting value, recording each iterate to more decimal places than required, to find a root to a stated accuracy
Justify the accuracy of a root by a sign change over the rounding interval, and recognise that some rearrangements give iterations that fail to converge
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