Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Americans pronounce carves as KARVZ (/kɑrvz/). You'll hear it in sentences like "He carves wooden figures using traditional whittling tools".
Record yourself saying "carves" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 4 sounds. Explore each sound's mouth shape and how it's made.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Open wide for the 'ah' vowel. Lift the tongue back and up while flaring the lips for the 'r'.
Lift your bottom lip so its inner edge (where the wet part meets the dry part) touches the very bottom of your top front teeth. Add vocal cord vibration as you blow air through.

Same position as S, but add vocal cord vibration. Feel the buzz.

The textbook way isn't wrong — it's just not how anyone actually says it.
Americans use a relaxed retroflex R — the tongue curls back rather than rolling. The R is one continuous sound with the vowel before it, not two separate sounds.