2026 CVSS P1 Q3

Find, in exact value, the equation of the tangent of the curve \(y=\ln\left(\dfrac{12x}{(2x-7)^2}\right)\) at the point \(x=4\).[6]

The tangent intersects the line \(y=-\dfrac74x+17\) at \(Q\). Show that the \(x\)-coordinate of \(Q\) is \(-1+\ln4\sqrt3\).[3]

Two points are given by \(P(-1,-10)\) and \(R(5,4)\). Calculate the area of triangle \(QPR\) to 1 decimal place.[3]