You went out and set up your fancy rig, with all of its shaders and its pixel core density modifiers -- you want to play games that will take full advantage of your hardware. We hear you.
So has Rockstar. DirectX 11 support headlines the latest title update for L.A. Noire: The Complete Edition, which should hopefully help you better decide the fates of the game's virtual persons of interest. You'll be able to switch between DirectX 9 and DirectX 11 renderers on the fly through the game launcher.