10 The equation of a circle is \(( x - 3 ) ^ { 2 } + y ^ { 2 } = 18\). The line with equation \(y = m x + c\) passes through the point \(( 0 , - 9 )\) and is a tangent to the circle. Find the two possible values of \(m\) and, for each value of \(m\), find the coordinates of the point at which the tangent touches the circle.
\includegraphics[max width=\textwidth, alt={}, center]{cacac880-5b44-4fae-8ed8-88a095db69cd-16_855_1600_306_233} A function is defined by \(\mathrm { f } ( x ) = \frac { 4 } { x ^ { 3 } } - \frac { 3 } { x } + 2\) for \(x \neq 0\). The graph of \(\mathrm { y } = \mathrm { f } ( \mathrm { x } )\) is shown in the diagram.

1. Find the set of values of \(x\) for which \(\mathrm { f } ( x )\) is decreasing.
2. A triangle is bounded by the \(y\)-axis, the normal to the curve at the point where \(x = 1\) and the tangent to the curve at the point where \(x = - 1\). Find the area of the triangle. Give your answer correct to 3 significant figures.
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