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The diagram shows the curve \(y = 2 x ^ { 2 }\) and the points \(X ( - 2,0 )\) and \(P ( p , 0 )\). The point \(Q\) lies on the curve and \(P Q\) is parallel to the \(y\)-axis.
- Express the area, \(A\), of triangle \(X P Q\) in terms of \(p\).
The point \(P\) moves along the \(x\)-axis at a constant rate of 0.02 units per second and \(Q\) moves along the curve so that \(P Q\) remains parallel to the \(y\)-axis.
- Find the rate at which \(A\) is increasing when \(p = 2\).