Calculus optimization problem:
Find the dimensions of the largest possible trapezoid, by area, that fulfills the following criteria:
- longer base runs along the x-axis
- other two vertices sit above the x-axis
- bounded by the quadratic function $4y = 16 - x^2$
For any $x \in (-4,4)$ the vertices are $(-4,0), (-x,\frac {16-x^2}{4}),(x,\frac {16-x^2}{4}),(4,0)$
$A = \frac 12 (8+2x)(\frac {16-x^2}{4})\\ \frac {dA}{dx} = ??? = 0$
Solve for $x$