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The diagram shows the curve \(y = \frac { \ln x } { x ^ { 4 } }\) and its maximum point \(M\).
- Find the exact coordinates of \(M\).
- By using integration by parts, show that for all \(a > 1 , \int _ { 1 } ^ { a } \frac { \ln x } { x ^ { 4 } } \mathrm {~d} x < \frac { 1 } { 9 }\).