Is it possible to max a companion’s approval rating

For the player, armor reduces the damage taken by physical attacks by 2 for every armor point in the campaign, or by 1 in multiplayer.

Armor on monsters reduces the damage taken by 1 per point.

Armor is applied after damage multipliers (like %-Attack, Crit, etc.) but before damage reduction from % melee defense.

The formulas for damage taken are:

For monsters: [WeaponDmg * (1 + Attk%) * (1 + CritDmg%) * (1 + FlankDmg%) * (1 + BarrierDmg%) * (1 + GuardDmg%) - Armor *(1 - ArmorPen%)] * AbilityMultiplier%

For the player: [BaseDmg * (1 + CritDmg%) * (1 + FlankDmg%) - Armor * 2(only in solo mode) *(1 - ArmorPen%)] * (1 - Defense%) * (1 - ElementalDef%)

Source: http://dragonage3.wiki.fextralife.com/Attributes

As your companions begin to approve of your decisions the outside of the tarot card turns from black to white. If you're romancing a NPC and you go on a personal quest, after completion the face of the card will change based on the decisions in the quest. I've found it difficult to gain full approval from all companions in one playthrough. It's not the same as DA2 due to the fact that if you get full approval from one character and no longer appears on the screen "Iron Bull Approves" if you choose something he disapproves his approval will go down again and not stay at full approval.