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\includegraphics[max width=\textwidth, alt={}, center]{69214874-18a7-495d-892d-2a0a7019cbe9-2_746_1182_1304_479}
The diagram shows the curve with equation \(y = x ^ { 3 } + 2 x ^ { 2 } - 13 x + 10\) and the tangent to the curve at the point ( 2,0 ).
- Find the equation of this tangent and verify that the tangent intersects the curve when \(x = - 6\).
- Calculate the exact area of the region bounded by the curve and the tangent.