The test function

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The test function

As a test case we will start with the function

$\begin{displaymath} f(x) \equiv \cos x - x = 0. \end{displaymath}$

(2)

How many different real solutions does the test problem have?

$\bgroup\color{red}\framebox{\em HAND CALCULATION}\egroup$ $\bgroup\color{black}$\phantom{0}$\egroup$ Modify the equation so that there are no solutions.

$\bgroup\color{red}\framebox{\em HAND CALCULATION}\egroup$ $\bgroup\color{black}$\phantom{0}$\egroup$ Modify the equation so that there are an infinite number of solutions.

$\bgroup\color{red}\framebox{\em HAND CALCULATION}\egroup$ $\bgroup\color{black}$\phantom{0}$\egroup$ Modify the equation so that there are two solutions, modulo $\bgroup\color{black}$2 \pi$\egroup$ .

We will look for a single solution $\bgroup\color{black}$x_0$\egroup$ in the interval $\bgroup\color{black}$[a,b]\equiv[0,\pi]$\egroup$ .

Charlie Macaskill 2004-07-26