Problem

The diagram shows part of the curve with equation $y=\dfrac{12}{\sqrt[3]{2x+1}}$. The point $A$ on the curve has coordinates $\left(\dfrac{7}{2},6\right)$.

(a) Find the equation of the tangent to the curve at $A$. Give your answer in the form $y=mx+c$.

(b) Find the area of the region bounded by the curve and the lines $x=0$, $x=\dfrac{7}{2}$ and $y=0$.