Will Final Cut Pro X run on 11" MacBook Air i5 4GB Memory 128GB Storage?

I'm about to replace my almost 5-year old Mid-2010 MacBook and I'm thinking of getting an Air since it's very compact. I only use my laptop for basic purposes (internet, iPhoto, iTunes, iPhone backup, etc.) but sometimes, I do basic video editing using Final Cut Pro X. Would an 11-inch MacBook Air running on i5, 4GB memory and 128 flash storage work well with FCPX? I'm planning to use an external hard drive with at least 1TB in case I do get the Air with the said tech specs. Also, how does upgrading to 8GB help?

I hope someone can help! I do not know much about specs. Thanks!