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\includegraphics[max width=\textwidth, alt={}, center]{16a5835e-002f-4c49-aacf-cda41c37f214-4_547_1057_255_543}
The diagram shows the curve \(y = \sqrt { } \left( x ^ { 4 } + 4 x + 4 \right)\).
- Find the equation of the tangent to the curve at the point ( 0,2 ).
- Show that the \(x\)-coordinates of the points of intersection of the line \(y = x + 2\) and the curve are given by the equation \(( x + 2 ) ^ { 2 } = x ^ { 4 } + 4 x + 4\). Hence find these \(x\)-coordinates.
- The region shaded in the diagram is rotated through \(360 ^ { \circ }\) about the \(x\)-axis. Find the volume of revolution.