A curve has equation \(y = 2 x ^ { 2 } - 5 x\).
The point \(P\) on the curve has coordinates \(( 1 , - 3 )\).
The point \(Q\) on the curve has \(x\)-coordinate \(1 + h\).
Show that the gradient of the line \(P Q\) is \(2 h - 1\).
Explain how the result of part (a)(i) can be used to show that the tangent to the curve at the point \(P\) is parallel to the line \(x + y = 0\).
For the improper integral \(\int _ { 1 } ^ { \infty } x ^ { - 4 } \left( 2 x ^ { 2 } - 5 x \right) \mathrm { d } x\), either show that the integral has a finite value and state its value, or explain why the integral does not have a finite value.