t=(4-x)/6 + (1+x^{2})^{1/2}/2.

Set the derivative equal to 0:

dt/dx= -1/6 + 1/2 * 1/2 * 2x * (1+x^{2})^{-1/2} = 0.

The solution is x=1/8^{1/2}.

y=4-x.