I gave up peeling potatoes years ago. I like new potatoes, red bliss, Yukon gold; the small ones. I guess they call them waxy potatoes. I scrub with a veg brush; eat skins and all. Very light or thin skins,
To bake, I use the Russet or mealy potatoes. Russets make better mashed potatoes, since the waxy kind just make glue. Since I rarely if ever, make mashed potatoes, I have an packet or two of Idahoan Instant Mashed on hand. Honestly, I can't tell the difference.
I would never peel the vitamins off a carrot. Just scrub clean with a veg brush.