Determine the two real roots of the equation \(8 x ^ { 6 } + 7 x ^ { 3 } - 1 = 0\).
Determine the coordinates of the stationary points on the curve \(y = 8 x ^ { 7 } + \frac { 49 } { 4 } x ^ { 4 } - 7 x\).
For each of the stationary points, use the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) to determine whether it is a maximum or a minimum.