4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4d5b914c-28b2-4485-a42e-627c95fa16e2-16_581_961_251_552}
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\caption{Figure 2}
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Figure 2 shows a sketch of the parabola with equation \(y = \frac { 1 } { 2 } x ( 10 - x ) , 0 \leqslant x \leqslant 10\) This question concerns rectangles that lie under the parabola in the first quadrant．The bottom edge of each rectangle lies along the \(x\)－axis and the top left vertex lies on the parabola．Some examples are shown in Figure 2.
Let the \(x\) coordinate of the top left vertex be \(a\) ．
（a）Explain why the width，\(w\) ，of such a rectangle must satisfy \(w \leqslant 10 - 2 a\)
（b）Find the value of \(a\) that gives the maximum area for such a rectangle．
Given that the rectangle must be a square，
（c）find the value of \(a\) that gives the maximum area for such a square．
Given that the area of the rectangles is fixed as 36
（d）find the range of possible values for \(a\) ．
\includegraphics[max width=\textwidth, alt={}, center]{4d5b914c-28b2-4485-a42e-627c95fa16e2-16_2255_50_311_1980}