10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e116a86f-63e0-4e80-b49c-d9f3c819ce15-24_872_1285_246_392}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Figure 3 shows a sketch of part of the curve with equation
$$y = 8 x - x ^ { \frac { 5 } { 2 } } \quad x \geqslant 0$$
The curve crosses the \(x\)-axis at the point \(A\).
- Verify that the \(x\) coordinate of \(A\) is 4
The line \(l _ { 1 }\) is the tangent to the curve at \(A\).
- Use calculus to show that an equation of line \(l _ { 1 }\) is
$$12 x + y = 48$$
The line \(l _ { 2 }\) has equation \(y = 8 x\)
The region \(R\), shown shaded in Figure 3, is bounded by the curve, the line \(l _ { 1 }\) and the line \(l _ { 2 }\) - Use algebraic integration to find the exact area of \(R\).