Tangent from signed derivative areas

The diagram shows the graph of \(y=\mathrm{F}'(x)\) for \(0\leq x\leq7\). The curve intersects the \(x\)-axis at \(x=2\) and \(x=5\), and passes through \((3,-4)\). The diagram is not drawn to scale.

The areas of regions \(A\), \(B\) and \(C\) are \(6\), \(5\) and \(3\) square units respectively.

1. Given that \(\mathrm{F}(0)=9\), find \(\mathrm{F}(7)\).[3]
2. The function \(\mathrm{h}\) is defined by \(\mathrm{h}(x)=\mathrm{F}(x^3-5)\). The curve \(y=\mathrm{h}(x)\) passes through the point \((2,k)\), where \(k\in\mathbb{R}\). Find the equation of the tangent to the curve at this point, giving your answer in terms of \(k\).[4]