Carver's starting approval rating is 
(+50); he will receive an unavoidable (+5) in prologue.
Friendship
Carver takes value in proving his worth to his family and comrades. Aggressive behavior impresses Carver, but on a similar note, a responsible Hawke that keeps his/her family out of trouble and allows Carver to make his own mark will gain friendship. He is adamant about an apostate Hawke avoiding the suspicion of the Order, thus supporting the Chantry's actions and siding with Templars over mages will net his approval despite his vocal disdain for the Templars themselves. In addition, choices which appeal to Carver's pride as a Fereldan or otherwise benefit other Fereldans will garner friendship with him.
Act 1
- Act of Mercy:
(+10) if Hawke refuses to help Grace and the others escape the Circle by murdering Ser Thrask.
Act of Mercy: a further
(+10) if Hawke returns the mages to the Circle upon exiting the cave. - The Deep Roads Expedition: (+10) if Hawke brings Carver along on the expedition.
The Deep Roads Expedition: (+5) if Hawke agrees to find the Wardens for Carver (only available if Anders was also brought on the expedition).
The Deep Roads Expedition: (+10)If you agree to rescue Sandal (Confirmed on as of patch 1.05). - Enemies Among Us: (+5) if Hawke kills Idunna after breaking the compulsion.
Enemies Among Us: (+5) if Hawke says he/she will tell the Templars that Keran may be possessed.
Enemies Among Us: (+5) if Hawke says, "I support the Templars." when talking to Knight-Captain Cullen upon returning to the Gallows (after completing the quest). - Family History: (+15) if when giving Carver the family letters Hawke avoids aggressive/direct dialogue choices.
- Friends in Low Places: (+5) if Hawke accepts Dougal's offer.
- Loose Ends (Athenril): (+5) if Hawke initially refuses the quest from Athenril (although accepting the quest afterwords with Carver in the party will result in a (+10) ((see rivalry as well)) )
Loose Ends (Athenril): a further (+10) if Hawke gives the boy Pryce the goods - Loose Ends (Meeran): (+5) if the quest was obtained from Meeran and Hawke spares Lord Harimann
Loose Ends (Meeran): a further (+5) if Hawke then returns to Meeran and tells him that the job was not complete. - Magistrate's Orders: (+10) if Hawke kills Kelder or (+5) if Hawke allows Fenris to kill him. (Available with Patch 1.04)
- Shepherding Wolves: (+5) if Hawke refuses to hand Ketojan over to the Qunari.
Shepherding Wolves: (+5) if upon returning to Sister Petrice Hawke says, "I don't care, just pay me." - Tranquility: (+10) if Hawke defers to Carver upon leaving Lirene's Fereldan Imports or (+5) if Hawke chooses the diplomatic dialogue option, "We're on the same side." instead of deferring to Carver (only available to a diplomatic Hawke) upon leaving Lirene's Fereldan Imports.
- The Unbidden Rescue: (+5) if Hawke agrees to rescue Saemus Dumar.
The Unbidden Rescue: (+5) if upon returning Saemus to the Viscount Hawke says, "Saemus is right to question." - Wayward Son: (+10) if Hawke defers to Fenris when dealing with Danzig and then kills him afterwards.
Wayward Son: (+10) if Hawke tells Feynriel to go to the Circle.
The total potential friendship points gained if Hawke sided with Athenril and Carver is brought into the Deep Roads is (+155).
Legacy DLC
- Malcolm's Will: (+15) When talking about your father not wanting a mage child Hawke chooses the diplomatic choice for the first part and diplomatic or sarcastic choice for the second or (+10) if Hawke chooses Sarcastic choices. There is a chance for (+25) if Carver's friendship is high enough and you choose all diplomatic dialogue options (also possible to make a sarcastic choice for the first part and a diplomatic choice for the second).
- Legacy (quest): Sides with Larius (+5)
Rivalry
Carver despises being inferior to his sibling, and so verbal put-downs and dialogue that makes Hawke "selfless" will make him dislike Hawke. Reckless and criminal behavior, as well as consorting with Kirkwall's seedier elements, will grate his nerves. He also does not approve of pro-mage options.
Prologue
- The Destruction of Lothering: Upon encountering Aveline and Wesley, (+5).
Act 1
- Act of Mercy: (+10) if Hawke agrees to kill Thrask when Grace asks (this is the only Rivalry gain along this route).
- Act of Mercy: (+10) if Hawke fights Ser Kerras to free Grace and the mages after refusing to kill Thrask (this negates the (+10) from that decision, cannot be avoided).
- An Errant Letter: (+5) if Hawke says, "Pay me or I'll expose you."
- Bait and Switch: (+5) if Hawke accepts the quest from Anso.
- Blackpowder Promise: (+5) if Hawke refuses to help Javaris.
- The Deep Roads Expedition: (+15) if Hawke does not bring Carver along on the expedition.
- Enemies Among Us: (+5) when talking to Knight-Captain Cullen upon returning to the Gallows, if Hawke says, "The Order needs to change"
- Family History: (+15) if the aggressive/direct reply is chosen after giving Carver the family letters
- The First Sacrifice: (+5) if Hawke sleeps with Jethann.
- Long Way Home: (+5) when Merrill used blood magic to open the barrier, if Hawke says, "It did help us."
- Loose Ends (Athenril): (+10) if Hawke accepts the quest
- Loose Ends (Meeran): (+10) if Hawke kills Lord Harimann
- Magistrate's Orders: (+5) if Hawke returns Kelder to his father.
- Tranquility: (+5) if Hawke says, "I help all my fellow mages."
- Tranquility: (+5) after exiting Lirene's Ferelden Imports, if Hawke choose the aggressive option. ("Don't question me!").
- The Unbidden Rescue: (+5) if Hawke refuses to rescue Saemus Dumar.
- The Unbidden Rescue: (+5) upon returning Saemus to the Viscount, if Hawke says, "Yes, your son went too far" or "You're both stubborn fools."
- Wayward Son: (+10) if Hawke allows Feynriel to go to the Dalish.
- Wayward Son: (+5) if Fenris gets information out of Danzig but then spares him.
Legacy DLC
- Legacy (quest): (+5) when talking about their father not wanting a mage child, Hawke chooses aggressive responses.
- Legacy (quest): (+5) if Hawke sides with Janeka.
- Legacy (quest): (+5) during the last conversation in Hawke Estate, if Hawke asks Templar Carver why he joined the Templar Order.