If the figure is visible, simply click on it to access the animation toolbar, in the center of which there is a slider that controls the animation.

If the figure is not visible, click on the button "Figure 3.8.13" to activate the animation code.

The 101 frames in the animation subdivide $a\=\sqrt{12}$, the semi-major axis of the ellipse, into 100 equal divisions, so that each frame increments $x$ by $0.034641$.

Within the resolution supported by this animation, the largest rectangle has width twice $x\=2.4595$, and area 7.7460. (See frame 72 in the animation.)

Write a sequence consisting of the objective function and the constraint equation.
Press the Enter key.

Context Panel: Optimization≻Maximize (local)

The graph of $A\left(x\right)$ in Figure 3.8.7(b) shows an absolute maximum of about 7 for $x\doteq 2.5$. The graph itself can be probed for a numeric estimate of the maximum point. Alternatively:

Write $2 x \sqrt{5\left(1-x^2\/12\right)}$ 
Context Panel:
Optimization≻ Optimization Assistant

See Figures 3.8.7(c) and 3.8.7(d).

Click  to launch the Optimization Assistant with all the data in place.

Write $A\left(x\right)\=\dots$
Context Panel: Assign Function

Write $A\prime \left(x\right)\=0$ and press the Enter key.

Context Panel: Solve≻Solve

Write the positive root.
Context Panel: Approximate≻10 (digits)

Evaluate $A$ at the critical number.
Context Panel: Evaluate and Display Inline
Context Panel: Simplify≻Simplify

Evaluate $A$ at the critical number.
Context Panel: Approximate≻10 (digits)

Expression palette: Evaluation template
Evaluate constraint ellipse at $x\=\sqrt{6}$
Press the Enter key.

Context Panel: Solve≻Solve

Write the positive solution.
Context Panel: Approximate≻10 (digits)