Consider the function ~f(x)=9-x^2~ f(x)=9−x 2 space, f, (, x, ), equals, 9, minus, x, squared, space for ~f(x) 0~ f(x)≥0 space, f, (, x, ), is greater than or equal to, 0, space only.

The shaded region is an isosceles triangle formed by joining the points ~(0,0), (0,0)space, (, 0, 0, ), ~big (x, f(x) big), (x, f(x))space, (, x, f, (, x, ), ), and ~big(-x, f(x) big) (−x, f(x))space, (, minus, x, f, (, x, ), ), where~0 x 3 0≤x≤3, 0, is less than or equal to, x, is less than or equal to, 3.

What is the area of the largest triangle that satisfies the stated conditions?