Find the maximum value of \(f(x,y) = x \sqrt{1 - y^2} + y \sqrt{1 - x^2},\)where \(-1 \le x, y \le 1.\)
Hint:
Because this is symmetric with respect to x and y, the maximum (and minimum) will occur when x = y.
Hence find the maximum of \(2x\sqrt{1-x^2}\)
