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The following figure shows part of the graph of the function \(f(x) = 2x^2\).

The figure is not to scale.

The line \(T\) is the tangent to the graph of \(f\) at \(x = 1\).

1. Show that the equation of \(T\) is \(y = 4x - 2\).
2. Find the x-intercept of \(T\).
3. The shaded region \(R\) is bounded by the graph of \(f\), the line \(T\) and the x-axis.
   1. Write down an expression for the area of \(R\).
   2. Find the area of \(R\).