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\includegraphics[max width=\textwidth, alt={}, center]{e32902b8-a259-4572-982e-2a35413b81b2-08_534_462_248_804}
The diagram shows part of the curve with equation \(y = \frac { 12 } { \sqrt [ 3 ] { 2 x + 1 } }\). The point \(A\) on the curve has coordinates \(\left( \frac { 7 } { 2 } , 6 \right)\).
- Find the equation of the tangent to the curve at \(A\). Give your answer in the form \(y = m x + c\). [4]
\includegraphics[max width=\textwidth, alt={}, center]{e32902b8-a259-4572-982e-2a35413b81b2-08_2716_38_109_2012} - Find the area of the region bounded by the curve and the lines \(x = 0 , x = \frac { 7 } { 2 }\) and \(y = 0\).