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## 'Root Hunter' printed from http://nrich.maths.org/

.

This graph is positive for $x = 5$ and negative for $x = 3$. This
means that the graph must cut the $x$ axis somewhere between $3$
and $5$.

Although in this case the result is obvious (because we have the
whole graph to look at!), we can also use this idea to show that
more tricky functions also have roots.

Use this idea to show that these functions possess at least one
solution $f(x) = 0$:

$$ f(x)=\frac{1}{x-2}+\frac{1}{x-3} $$ $$f(x)= x^x - 1.5 x$$
$$f(x)= x^{1000000}+{1000000}^x - 17$$ $$f(x)=\cos(\sin(\cos x)) -
\sin(\cos(\sin x)) $$

Optional extension activity: Can
you make a spreadsheet that helps you find the numerical values of
the roots to, say, four decimal places?