The answer is no -- that notebook cannot output 4K video.  Even if it were technically possible, the weak GPU would be completely overwhelmed with the task of rendering high resolution video.  
Hello Everyone, I have a question regarding an old dinosaur and the requirements of modern-day technology. I have a old Inspiron 4010 14R that I have been chugging along since its first breath of life back in 2010. Recently a older HD monitor that I have been using for about as long as my laptop as an external monitor broke and I need to purchase a new model. My question pertains to whether an old laptop like my own could properly display its contents on a 4K resolution monitor? I believe I may already have my answer from a similar question for another computer on a different forum but I would like to confirm my suspicions for my particular model. I have no idea about the generation of the HDMI port but I assume because of its age its one of the first types to be put in laptops and of course there is only a first generation Intel HD graphics card within the computer. The native resolution of the factory monitor is 1366x768. Even though I was able to extend the picture and quality up to 1920x1080 on my old monitor I believe that I may not have that type of luck on a 4K monitor. Still if I can go with 4K for the future I would like to take that step or I can go the FHD route if that doesn't work. Thank you everyone for all your input.
Connect an old laptop (Inspiron 4010 14R) to a 4K monitor?