I would not use dips as a max effort exercise, it would be better used as an assistance exercise.
You could do the overhead press, incline press, floor press, a press off of pins from your sticking point as other max effort exercises.
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Also are there two parts of the triceps that are worked seperately or is both sides worked at the same time?
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There are three heads to the triceps. They are all generally worked together. You can target the long head of the triceps a little differently since it crosses the shoulder joint and is an extender of the shoulder as well as the elbow.
Doing exercises using both elbow and shoulder extension will train the long head of the triceps more.
Doing exercises that limit the movement to extension of the elbow joint will train the long head less. There are some arguments that doing an exercise this way will target the 2 shorter heads of the triceps more. Though there are good arguments on both sides.
All of the triceps are trained using each of the above methods, the above are just ways to train them a little differently.