Mathematics

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

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

1. Show that the equation of \(T\) is \(y= 4x -2\).[5]
2. Find the \(x\)-intercept of \(T\).[2]

3. The shaded region \(R\) is enclosed 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 \(R\).[9]