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The diagram shows the curve \(y = 1 - x + \frac { 6 } { \sqrt { x } }\) and the line \(l\), which is the normal to the curve at the point (1, 6).
- Determine the equation of \(l\) in the form
$$a x + b y = c$$
where \(a\), \(b\) and \(c\) are integers whose values are to be stated.
- Verify that the curve intersects the \(x\)-axis at the point where \(x = 4\).
- In this question you must show detailed reasoning.
Determine the exact area of the shaded region enclosed between \(l\), the curve, the \(x\)-axis and the \(y\)-axis.