The Collaborative International Dictionary of English v.0.48:

Maximum \Max"i*mum\, n.; pl. Maxima. [L., neut. from maximus
   the greatest. See Maxim.]
   The greatest quantity or value attainable in a given case;
   or, the greatest value attained by a quantity which first
   increases and then begins to decrease; the highest point or
   degree; -- opposed to minimum.
   [1913 Webster]

         Good legislation is the art of conducting a nation to
         the maximum of happiness, and the minimum of misery.
                                                  --P.
                                                  Colquhoun.
   [1913 Webster]

   Maximum thermometer, a thermometer that registers the
      highest degree of temperature attained in a given time, or
      since its last adjustment.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Maximum \Max"i*mum\, a.
   Greatest in quantity or highest in degree attainable or
   attained; as, a maximum consumption of fuel; maximum
   pressure; maximum heat.
   [1913 Webster]

WordNet (r) 3.0 (2006):

maximum
    adj 1: the greatest or most complete or best possible; "maximal
           expansion"; "maximum pressure" [syn: maximal,
           maximum] [ant: minimal, minimum]
    n 1: the largest possible quantity [syn: maximum, upper
         limit] [ant: lower limit, minimum]
    2: the greatest possible degree; "he tried his utmost" [syn:
       utmost, uttermost, maximum, level best]
    3: the point on a curve where the tangent changes from positive
       on the left to negative on the right [ant: minimum]

Moby Thesaurus II by Grady Ward, 1.0:

205 Moby Thesaurus words for "maximum":
   abundance, acmatic, acme, affluence, all, ample sufficiency,
   ampleness, amplitude, apex, apical, apogee, authority,
   authorization, avalanche, be-all and end-all, best, blue ribbon,
   bonanza, bountifulness, bountiousness, brow, bumper crop, cap,
   capital, ceiling, championship, chief, climactic, climax,
   cloud nine, command, comprehensive, consequential, considerable,
   consummate, control, copiousness, crest, crown, crowning, culmen,
   culmination, deep, directorship, dominion, edge, effectiveness,
   end, exhaustive, extravagance, extreme, extreme limit, extremity,
   exuberance, fertility, first place, first prize, first-class,
   first-rate, flood, flow, foison, full, full measure, fullness,
   generosity, generousness, grand, grave, great, great abundance,
   great plenty, greatest, gush, head, headmost, headship, heaven,
   heavens, heavy, hegemony, height, high noon, highest,
   highest degree, highest pitch, highest point, imperium, influence,
   intense, irresistible, jurisdiction, kingship, landslide,
   lavishness, leadership, liberality, liberalness, limit, lordship,
   lots, luxuriance, main, management, mastership, mastery, maximal,
   meridian, meridional, mighty, more than enough, most, mountaintop,
   much, myriad, myriads, ne plus ultra, new high, no place higher,
   noon, nth degree, numerousness, opulence, opulency, outpouring,
   outside, overflow, overmost, palms, paramount, paramountcy, peak,
   pinnacle, pitch, plenary, plenitude, plenteousness, plentifulness,
   plenty, point, pole, power, powerful, preeminent, presidency,
   prevalence, primacy, prodigality, productiveness, profuseness,
   profusion, quantities, record, repleteness, repletion,
   rich harvest, rich vein, richness, ridge, riot, riotousness, rule,
   say, scads, serious, seventh heaven, shower, sky, sovereignty,
   spate, spire, stream, strong, substantiality, substantialness,
   summit, summital, superabundance, superlative, supremacy, supreme,
   sway, teemingness, the whole, tip, tip-top, top, top spot,
   top-notch, topmost, total, ultimate, upmost, upper extremity,
   upper limit, uppermost, utmost, utmost extent, uttermost, vertex,
   vertical, very top, wealth, zenith, zenithal