American Motors Corp. yesterday reported that it earned a $1.2 million profit in the final three months of 1976 in a sharp reversal from the record $51.1 million loss in the previous quarter.

The 4-cent-a share profit in the first quarter came despite the costly price cuts and cash rebates the smallest of the U.S. auto makers has begun to stimulate sluggish small-car sales.

AMC's fiscal year begins in October.

AMC chairman Roy D. Chapin Jr. and president William V. Luneburg said the profits resulted from a continuation of cost reduction actions to lower its automotive segment break-even point, and the continued profitability of its AM General Corp. and other subsidiaries.

The No. 4 auto firm's first-quarter profits came on sales of $559 million, a 9 per cent drop from the previous year. In the year-ago October-December quarter, AMC earned $7.5 million.

In the 1976 fiscal year, the auto firm lost $46.3 million to finish in the red for the second year in a row.

AMC, whose share of the domestic market droped from 4.6 per cent in 1975 to 2.8 per cent last year as interest in small cars waned, slashed $253 from the price of its subcompact Gremlin in November and is offering $253 cash rebates on its Pacer and Hornet wagon models.

Atlantic Richfield Co. reported a sharp earnings increase for 1976 over 1975. Fourth-quarter earnings also advanced over the previous year.

Earnings from regular operations for the nation's eight largest oil company rose by 30 per cent in 1976 to $453.18 million ($3.97 a share). However, a one-time gain of $122 million ($1.07) from the sale of some Canadian assets and domestic property boosted earnings to $575.18 million ($5.04) last year. In 1975, Arco earned $350.4 million, ($3.08). Revenues in 1976 reached $8.92 billion against $7.75 billion the year before.

In the fourth quarter, the coroporation's earnings rose by 9 per cent to $124.87 million ($1.09) from $114.34 million ($1) a year earlier. Fourth-quarter revenues were $2.40 billion in 1976 and $2.09 billion in 1975.

DuPont Co. earnings for 1976 rose by 71 per cent to $9.30 a share from $5.43 a share in 1975. Fourth quarter earnings declined, however, reflecting weakness in the fiber sector.

For the 12 months, DuPont earned $459 million, up from $272 million in 1975. Sales rose by 16 per cent to $8.361 billion from $7.22 billion, reflecting a 10 per cent advance in physical volume and a 5 per cent rise in selling prices.

For the fourth quarter, net income came to $93 million ($1.87 a share), down from $141 million ($2.87) in the closing 1975 quarter. Sales rose 5 per cent from $1.955 billion to $2.055 billion.

Irving S. Shapiro, chairman of the board, cited the improved overall performances of the company's chemicals, plastics and specialties businesses.

The 3M Co.'s net income in the fourth quarter of 1976 jumped 62.9 per cent over the same period of 1975. Both the fourth quarter and 1976 results were records.

The company said fourth-quarter net income was $88.9 million (77 cents a share) compared with $54.6 million (48 cents) in the fourth quarter of 1975. Sales were $875.4 million against $780.8 million.

For the full year, net income totaled $338.5 million ($2.94) up 28 per cent from $264.5 million ($2.31) in 1975. Sales in 1976 were $3.51 billion, 12.4 per cent on 1975 sales of $3.13 billion.

American Express Co. reported that its 1976 profits rose 18 per cent over 1975 results, boosted by a sharp increase in fourth-quarter earnings.

The international banking and travel service firm said its 1976 profits climbed to $194.5 million ($2.70 a share) from $165 million ($2.29) a year earlier. Revenues rose from $2.49 billion in 1975 to $2.95 billion.

Annual earnings were lifted by a strong fourth quarter, when profits reached $55.5 million (77 cents), up 43 per cent from $38.8 million (54 cents) in the fourth quarter 1975. Fourth-quarter revenues advanced to $785.6 million from $667.6 million a year earlier.

E. F. Hutton Group, Inc., the holding company for the nation's second largest brokerage firm, yesterday said its 1976 profits were 17 per cent larger than 1975 results.

Fourth-quarter profits were up 38 per cent over a year earlier.

E. F. Hutton's earnings for the full year totaled $23.53 million ($3.88 a share) against $20.14 million ($3.39) in 1975. Revenues advanced from $253.13 million to $314.67 million.

In the fourth quarter, earnings rose sharply to $5.01 million (82 cents) on revenues of $76.56 million from $3.61 million (61 cents) on revenues of $63.05 million a year earlier.

The company said investment funds such as options and tax shelters were major factors in the earnings improvement. Hutton also reported a 20 per cent year-to-year increase in revenues from securities commissions.