Should Central Bank just focus on managing inflation or also target financial stability?

In Indian scenario, where there is democracy, as an apex bank of the country, the central bank should perform both the functions i.e. it should manage the inflation as well as it should plan  & implement on the measures of financial stability for exa. credit control, currency valuation, etc.

Central Banks need to focus on Inflation, unemployment, maintainance of asset prices, currency value and credit policies leading to easy flow of credit and moreover stability for Financial Institutions.

Then the problem lies in the Political interference like that happened in US which trigered the Subprime crisis. There prior to 1993 everything was going fine when President Clinton bought in his political agenda through the Housing and Urban Development (HUD) department of the Federal Government where he appointed a Secretary called Linda Achtenberg and Russian immigrant to head it. She was vociferous to giving housing to the poor and started regulating Banks to lend to the poor even to those who cannot afford Housing. She penalised banks who didn't comply, not permiting them to open branches or troubling them in mergers and other growth activities if they didn't comply. So the Banks loosened their lending standards and the subprime mortgage problem started. Later on everyone stood in line to implement the Clinton political will and the Investment Banks came up will sorts financial instruments to support this and when the poor couldn't pay the mortgage the houses were impounded and sold cheap leading to lowering of prices on houses and the problem of deflation of housing prices started and led to the demise of these great institutions which otherwise was in stable situaiton. Presidient Bush came in and catalyzed Clintons ideas by pursuing the same political will.

The morale even if the Central Banks do their jobs sometimes political will can interfere and cause instability.

Inflation management is essential for financial stability.  Both go hand in hand.  Hence the central banks of the world have to achieve both for financial prosperity and balance.

Financial stability is currently regarded, parallel to the inflation target, as the main task of a central bank.
If you see, the financial system has essentially three main tasks: converting savings into financing, managing risk and providing efficient channels of payment. e.g. A bank receives savings from households which it then lends to other households or to companies that need to invest. Banks are specialists at valuing, monitoring and managing credit risks in the households and companies to which they lend. The bank therefore contributes to ensuring that the mediation of capital in the economy functions efficiently; it is sufficient that borrowers can convince the bank of their creditworthiness, they do not need to convince each individual saver. Similarly, savers do not have to assess the creditworthiness of every borrower; it is enough to be satisfied of the bank's solvency. The banks can also supply payment services for households and companies by using the existing financial infrastructure, such as accounts and various routines for transferring funds between financial institutions.
As these functions are central to an efficient economy, it is evident that major problems can arise if financial stability is upset.