italy-esame-di-stato 2018 Q5

italy-esame-di-stato · Other · esame-di-stato__matematica Stationary points and optimisation Geometric or applied optimisation problem
5. With a fence 2 metres long, one wants to enclose a surface having the shape of a rectangle topped by a semicircle, as in the figure: [Figure]
Determine the dimensions of the sides of the rectangle that allow enclosing the surface of maximum area.
5. With a fence 2 metres long, one wants to enclose a surface having the shape of a rectangle topped by a semicircle, as in the figure:\\
\includegraphics[max width=\textwidth, alt={}, center]{9c1becc2-d505-467f-bee3-3bef03778b0a-4_336_309_1366_877}

Determine the dimensions of the sides of the rectangle that allow enclosing the surface of maximum area.