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I have a DELL E7450 laptop connected via an HDMI cable to a DELL UP3214Q monitor (which can display 3840x2160 @ 60Hz with a DP1.2 cable) . Ubuntu 14.10 uses the 3840 X 2160 resolution just fine - although @ 30Hz (which I don't mind). No drivers required. xrandr shows:

HDMI1 connected 3840x2160+1920+0 (normal left inverted right x axis y axis) 698mm x 392mm

   3840x2160      30.0*+   25.0     24.0     30.0     24.0  

   1920x1200      60.0  

But Windows 7 64-bit only sees 1920x1080 as the maximum resolution. The Intel HD Graphics 5500 settings allow for custom resolutions, but the maximum I could set was 2560 x 1440 @ 30Hz. Beyond that, everything would error with

The custom resolution exceeds the maximum bandwidth capacity

This error is obviously completely bogus!

Also, I accidentally managed to get 3840x2160 @ 30Hz as a regular resolution in Control Panel after I booted back from Ubuntu into Windows once. This trick didn't work after rebooting windows once again to install some updated. I hadn't installed anything else in Windows, or changed any settings. Before booting into Ubuntu, I had rebooted Windows several times, so I'd rule out rebooting itself as a solution. Could Ubuntu have written some information to the graphics card or the monitor?

Other things I've tried - nothing worked:

• Installed the Dell Display Manager: it can't do anything about resolutions


• Installed Entec PowerStrip. It detects the maximum resolution but can't set it, even after adding it from Custom Resolution.
  
  


• tried to install Intel's native HD Graphics driver, but is says "The driver being installed is not validated for this computer. Please obtain the appropriate driver from the computer manufacturer."


• updated Dell's Intel HD video driver
  


• I've already installed the monitor driver and the monitor shows correctly by name in Device Manager. Still, no native resolution shows up anywhere.


• 
  Custom Resolution Utility allegedly doesn't work on Intel graphics cards. I've run, and it gave no error about the graphics card being Intel. It flickered the monitor and ultimately reset it 1920x1080, but didn't help at all with 4K.


• 
  Display Changer - seems to just pick up whatever resolutions are in the Registry


• disconnect the laptop's internal display, and only "connect to projector"

There's an Intel Community thread on the buggy "The custom resolution exceeds the maximum bandwidth capacity", but the Intel rep there isn't listening.

This is a nearly $2000 4K monitor that doesn't display 4K in Windows 7.

What else can I try?

The only thing that has worked so far was buying a Mini-DisplayPort to DisplayPort 1.2 cable. 3840x2160 @ 60Hz works great now.

It's disappointing that the Intel folks refuse to acknowledge the "maximum bandwidth exceeded" bug.

The Intel HD Graphics 4000 drivers for Windows allow the creation of custom resolutions. (I know, why on earth would it not recognize the 4k standard like Linux does!?)
Anyhow, on this dialog box create a 3840 x 2160 pixel resolution at 24Hz AND(!!) Select CVT-RB as the Timing Standard.
It should ask you to confirm, then close that app. Next time you plug in the monitor (it does have to be rediscovered by Windows) and open up the Windows Display Settings dialog box, pick the 4k monitor, in resolution, you will have the option to pick 3840x2160 - it should even have the tag 'Recommended'.

Intel HD Graphics 4000 can handle 4K @ 30p Hz with this steps and special Monitor

• Mac Mini Late 2012 with "Intel HD Graphics 4000"


• Boot Camp Installation of Windows 7



• Install Intel HD Graphics 4000 Drivers version 9.17.10.3347 (Legacy)
  find this inside Boot Camp @ support.apple.com/kb/DL1720?locale=en_US
  Path: BootCampDriversIntelBootCamp5.1.5621.zipBootCampDrivers




• Samsung Monitor 4K U28E590
  This the the trick! This monitor have Picture in Picture Option.




• From the windows Bar Open Intel Graphics Properties



• Advanced Mode


• Display --> Custom Resolutions


• Width=1920, Height=2160, Color Depth=All Colors,
  Refresh Rate=30, Timing Standard=CVT-RB ---> Add



• Restart your Computer.




• Connect both cables Mini-Port--> HDMI, and HDMI-->HDMI to this monitor



• On the monitor turn on Picture in picture and split in two the screen


• On Windows, Rich click on the Desktop --> Screen resolutions and arrange
  both displays like this image
  

Hope this helps

Now I need to figure it out how to do this on OS X El Capitan, cause I know tha is a fact that this Video Card is fully capable of 4K with this Monitor :)