Among the curves connecting the points (1, 2) and (2, 8), let γ be the curve on which an extremal of the functional
\(J[y]=\displaystyle\int_1^2\left(1+x^3 y^{\prime}\right) y^{\prime} d x\)
can be attained. Then which of the following points lie on the curve γ?
1
(√2, 3)
2
(√2, 6)
3
\(\left(\sqrt{3}, \frac{22}{3}\right)\)
4
\(\left(\sqrt{3}, \frac{23}{3}\right)\)