Major banks across the nation joined yesterday in raising their prime interest rates to 11 3/4 percent, just a quarter of a percentage point below the record 12 percent high set during the 1974-75 recession.

The increase set to rest any doubts on whether the rise would take hold throughout the industry. The jump from 111/2 percent was announced by Chemical Bank of New York last week, but others were slow to follow.

The moves revived debate about how much further interest rates can climb without having a significant impact on the economy. Yesterday's rise was the 15th this year. Lwast January, the prime was 73/4 percent.

Most analysts believe the prime rate will rise another one to 11/2 percentage points before finally peaking some time next year. The prime is the fee banks charge their most credit worthy corporate customers.

Interest rates are being pushed up by two forces: pressure from high loan demand, and credit-tightening moves by the Federal Reserve Board to help combat infaltion.

Speculation this week was that the Fed soon will be forced to boost interest rates another notch. Although the central bank has not commented on its policies, analysts said it was exerting upward pressure in the markets last week.

The board's Federal Open Market Committee, which sets operating policies for the monetary authority, voted at its Dec. 8 meeting to keep money and credit polcies tiht despite the recent slowdown in money supply growth.

Experts say if the tightening in the money markets continues, the board will have to take action on interest rates by raising its discount rate, the interest it charges on overnight loans to member banks.

Yesterday's increases appeared to have the blessing of the Carter administration. Although some officials had protested the Fed's tightening actions earlier, policymakers since have endorsed its tight-money policies.

Doubts about whether Chemical Bank's increase would hold came when Citibank, the nation's second largest bank and usually a leader in prime rate changes, failed to follow the increase on Friday.

However, yesterday a strin of other banks announced they were joining Chemical's move, including Bank of America, the nation's largest, and others, ranging from Chase Manhattan and Morgan Guaranty to Marine Midland of Chicago.

The extent of the increase in interest rates is a major factor in the overall economic outlook for next year. Analysts say there's room for some further rise, but they warn too far a jump could speed the recession.

Most analysts are predicting a mild recession will begin sometime next autumn, with the economy likely to grow by a sluggish one to 2.5 percent in 1979 and inflation apt to top 7.5 to 8 percent.

Although the prime rate doesn't directly determine the level of other interest rates, such as home mortage rates, it does serve as a benchmark against which other money costs can be measured