of or being a maximum; greatest possible; highest.

1880–85; maxim(um) + -al1

maximally, adverb
postmaximal, adjective
submaximal, adjective Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
maximal (ˈmæksɪməl)
1.  of, relating to, or achieving a maximum; being the greatest or best possible
2.  maths (of a member of an ordered set) being preceded, in order, by all other members of the set

Collins English Dictionary - Complete & Unabridged 10th Edition
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Word Origin & History

1882, see maximum.
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Medical Dictionary

maximal max·i·mal (māk'sə-məl)

  1. Of, relating to, or consisting of a maximum.

  2. Being the greatest or highest possible.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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Example sentences
It emphasizes maximal conservation of resources and government regulation to
  the near exclusion of other approaches.
Only when someone has a serious investment in resources and time does the
  incentive arise for working to maximal capacity.
We'll also be able to determine the maximal level of caloric restriction.
Singer selects research projects that can be exploited for maximal emotional
  impact and portrays them as the norm.
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