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\includegraphics[max width=\textwidth, alt={}, center]{1a4ddaa9-1ec2-4138-bfcb-a482fe6c942f-3_849_565_1466_790}
The diagram shows part of the curve \(y = 8 - \sqrt { } ( 4 - x )\) and the tangent to the curve at \(P ( 3,7 )\).
- Find expressions for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\int y \mathrm {~d} x\).
- Find the equation of the tangent to the curve at \(P\) in the form \(y = m x + c\).
- Find, showing all necessary working, the area of the shaded region.