My little car did pretty well in the mountains. I had to turn overdrive off quite a bit on both uphills and downhills, and occasionally even needed to go down into second gear. Once, as I was leaving Central City (which seems to be in a deep ditch at the top of the mountain), I realized I would never get out of there without going down into first gear, but that was the only time I had to take such drastic action.
I find the driving a bit challenging sometimes as there are two lanes, but the right hand one has trucks chugging along at around 45 miles an hour, and the left one has people driving incredibly fast at 75 mph, so a Corolla like me has to change lanes quite a bit, to keep my momentum up (if I slow down behind a truck, it would be impossible for me to get my speed back.) The speed limit is usually 65 mph, but I can't do that on the uphills usually.
These two photos are from rest stops and viewing points along the road.
Crossing the continental divide is interesting, as you're in a big tunnel when you do! They mark the spot with a green sign on the wall of the tunnel, and once you're through there's a relentless downhill.
Here's my car at the entrance of a canyon that I have forgotten the name of (Glenwood?) and my guide books are still in the car so I can't check. It was neat driving through this canyon, it had some short tunnels, and a river running through it.
This photo above is from the same rest stop just at the start of the canyon.