absolute
agreed, recommended
Do not exceed the recommended maximum of twelve drops a day.

legal, statutory

achieve, reach, rise to
The temperature reached a maximum of 35°C yesterday.

exceed
allow (sb/sth), permit (sb/sth)
In the exam, allow yourself a maximum of 30 minutes per question.
the maximum permitted speeds

limit sth to, restrict sth to
The amount you have to pay will be limited to a maximum of £500.

above (the) maximum, below (the) maximum
at (the) maximum
a drive of four hours at the maximum

to (the) maximum
He is using his talents to the maximum.

(up) to a/the maximum
maximum of
You can claim the allowance for a maximum of six months.

maximum possible
Everyone should contribute the maximum possible.

Maximum is used with these nouns:
advantage, altitude, amount, benefit, capacity, comfort, depth, distance, dose, duration, effect, effectiveness, efficiency, enjoyment, expansion, exposure, extent, fine, flexibility, force, freedom, height, impact, intensity, investment, length, level, leverage, limit, load, number, output, penalty, percentage, performance, potential, productivity, profit, protection, publicity, quantity, range, rebate, resolution, return, sentence, size, speed, strength, temperature, threshold, use, velocity, volume, width, workload