Will this RAM work in my laptop?

So I'm running this machine:
http://www.pcworld.idg.com.au/review...review/432342/ , it's got about 800mhz DDR3 RAM, totaling 6gb (one 2gb stick and one 4gb stick)
I'm trying to figure out if I can swap in some DDR4 2400mhz RAM, or if this laptop will even recognize it. Does it support that kind of memory? And what's the actual ceiling here—is it 8 or 16GB? I've heard a dozen different things online and I don't want to waste my money on parts that won't work.

Edit: Here’s the motherboard info, if that helps anyone: Dell Technologies 0 XWH1P (U3E1)

It’s running on DDR3 RAM at 1600MHz (800x2, since it's DDR). You can max it out at 16GB total by popping in two 8GB sticks.

Forget about DDR4. I don't know where you're getting your info, but DDR4 won't even fit in the slot, let alone work with the controller. And if you think the extra speed of DDR4 is going to change your life—don't bother. Even if you could actually install it, you wouldn't feel a lick of difference.

If you actually want to see a performance boost, just grab an SSD.

So DDR4 isn't an option... but regarding this DDR3, can I use any speed? Like, say 2400MHz? What’s actually the highest speed DDR3 can handle? Look, maybe these are stupid questions, but I'm definitely no tech expert here.

It officially supports up to 1600MHz, which is basically the fastest you can find through standard retail channels here in the States. Sure, there’s an 1866MHz DDR3 SO-DIMM out there, but it’s way more expensive, harder to track down, and who knows if your system will even play nice with it? Besides, you won't notice any real-world difference. The only place you might theoretically see a tiny bump is in gaming if you're running integrated graphics—and even then, the gains would be negligible since we're talking about older hardware.

Alright... so it’s got integrated graphics, but there’s also a Radeon HD 7650M tucked in there too. Not that I really care much, though—I don't spend a ton of time gaming anyway.
And about that SSD you mentioned... right now I'm running on an HDD. What do you think—can I just slap an SSD in there and have them both running at once? I don't want to toss the hard drive because I've got 1TB on it. I was looking stuff up online and saw people swapping out their optical drives for an SSD caddy to hold the extra drive. Think that would work on my laptop?

Upgrading to faster RAM won't do much for you since your laptop relies on a dedicated GPU for any real 3D work.

You can swap out the optical drive for an SSD, but you'll need a 12.7mm caddy—check yours first to be sure by pulling it out and measuring.

You can pick one up at Best Buy or find it way cheaper on eBay. Don't stress about finding one specifically labeled for your exact laptop model; these things are universal. There are really only two sizes: 9.5mm and 12.7mm. I'm betting you need the latter, but just measure it to be certain. Some sellers try to pull a fast one by charging a premium for "model-specific" caddies when they're actually just the same $4 part.

My advice? Put the SSD in the main hard drive slot and toss the old HDD into the caddy. Usually, the primary slot is SATA3 while the optical drive is limited to SATA2. You don't want to bottleneck your SSD, whereas the old HDD won't even notice the slower SATA2 speeds.