Intel(R) Core i5-2450M CPU @2.50GHz
INTERNAL- Intel HD Graphics 3000
DEDICATED- Radeon (TM) HD 7670M
in device manager both the display adapters are shown to be working properly.
but i think that my RADEON graphic card is not working. please tell me how to know which graphic card is working in my system.
On the display tab in dxdiag, only the Intel HD Graphics 3000is being shown.
Since you have a laptop, power saving is a big priority. As such, the 7670m is shut down most of the time to save power, it only turns on when there is a high graphics load, such as a game. You can force the 7670m on all the time by setting your laptop to high performance power mode, and disabling the Intel HD 3000, but that will burn through your battery quicker. Are you suffering poor performance in games? If so, which ones? The 7670m isn't that fast, with really demanding games, the 7670m will choke if you push your graphics settings too high.
More information needs to be given. What do you mean by "not working?" Just because it doesn't show up in DXDIAG doesn't mean anything. Do you still have options to configure the switchable graphics through the AMD control panel? If so, have you assigned applications to the "High Performance" settings? If you have done this, and you try to run a game, does the game run better than if you have it set to "Power Saving?" If it does, then your switchable graphics is working fine.
If, for some reason, you notice no performance increase, it is possible that you have the switchable graphics disabled and you are probably on a battery. There is a BIOS setting for that, you can see an example here: http://imageshack.us/photo/my-images/268/79500144.jpg/
Edit: Dxdiag, along with Windows Experience Index, is no way to gauge the performance of and functionality of your computer with any switchable graphics. You can get logs from dxdiag that can help solve conflict or driver issues but that's about it.