Question 37
determine the maximum value of the function
$$
f_k(x, y) = (x + y) - (x^{2k+1} + y^{2k+1})
$$
over all real numbers $x$ and $y$ satisfying the equation $x^2 + y^2 = 1$ for all positive integers $k$.
$$
f_k(x, y) = (x + y) - (x^{2k+1} + y^{2k+1})
$$
over all real numbers $x$ and $y$ satisfying the equation $x^2 + y^2 = 1$ for all positive integers $k$.