Consider the function $~f(x)=9-x^2~$ for $~f(x)\ge0~$ only.
The shaded region is an isosceles triangle formed by joining the points $~(0,0)\,$, $~\big(x,f(x)\big)\,$, and $~\big(-x,f(x)\big)$, where$~0\le x\le3$.
What is the area of the largest triangle that satisfies the stated conditions?
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