Question

A rectangle is bounded by the x- and y-axes and the graph {eq}y = displaystyle frac{6 – x}{2}

{/eq}. What should be the length and width of the rectangle so that its area is maximum?

EXPERT ANSWER

Let’s call the length {eq}x

{/eq} and the width {eq}y

{/eq}. Then the area of the rectangle is

{eq}begin{align*}

A &= xy \

&= x left ( frac{6 – x}{2} right ) \

&= 3x – frac12 x^2

end{align*}

{/eq}

This area function that we’ve