Without a monitor connected to it, your new Mac Mini is little more than a shiny paperweight. The Mac Mini supports up to two displays at resolutions up to 2,560 by 1,600 pixels. Attaching a monitor to a Mini running OS X Yosemite is as simple as plugging a compatible cable into the computer and powering it up. Before you go plugging in your monitor, however, it's essential that you verify that you're using a cable that's compatible with the Mac Mini.
Examine the cable connection on your monitor. The Mac Mini has native display support for Apple monitors with DisplayPort or ThunderBolt connections and with third-party monitors with HDMI and DisplayPort connections.
Obtain a display adapter, if necessary. If your monitor only has a DVI connection, for example, you need to obtain a Mini DisplayPort to DVI adapter. As of the date of publication, Apple no longer includes this adapter with the Mac Mini.
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Connect your monitor to the Mac Mini and turn the computer on. Wait for the Mac Mini to boot up and adjust its display settings to accommodate your monitor.
Open the Display settings screen to customizing your display settings. This step is optional. By default the Mac Mini selects the highest display resolution that's compatible with your monitor. However, some people benefit from using scaled resolutions, which improves legibility by increasing the size of items on the screen. Click the "Apple" menu in the top corner of your screen and select "System Preferences." Click "Displays" in the System Preferences window and then select "Displays" again. Click "Scaled" and choose the resolution you want to use with your monitor.