Mildred Pierce

From the trailer for the film
While the novel is told by a third-person narrator in strict chronological order, the film uses voice-over narration (the voice of Mildred). The story is framed by Mildred's interrogation by police after they discover the body of her second husband, Monte Beragon. The film, in noir fashion, opens with Beragon (Zachary Scott) having been shot. He murmurs the name "Mildred" before he dies. The police tell Mildred (Joan Crawford) that they believe the murderer is her first husband, Bert Pierce (Bruce Bennett). Bert has already been interrogated, and confessed to the crime. Mildred protests that he is too kind and gentle to commit murder, and goes on to relate her life story in flashback.
Mildred was married to Pierce, who is presently unemployed. Bert had been a real estate partner of Wally Fay (Jack Carson). Mildred has been supporting her family by baking and selling pies and cakes. Bert accuses Mildred of caring more about their daughters, and making them her priority instead of her husband. Mildred admits this, and the two decide to separate.
Wally propositions Mildred the moment he learns that she and Bert separated. Mildred retained custody of her two daughters, the 16-year-old Veda (Ann Blyth), a bratty social climber and aspiring pianist, and 10-year-old Kay (Jo Anne Marlowe), a tomboy. Mildred's principal goal is to provide for Veda, who longs for possessions that her mother can't afford, and social status above that of her family. She is ashamed of her mother's work as a baker.
Mildred searches for a job, but is hampered by her lack of employable skills. She has never worked outside her home except for her small baking business. The best she can find is as a waitress â a fact she hides from Veda. One day, Veda gives their maid, Lottie (Butterfly McQueen), Mildred's waitress uniform, with full knowledge that it's Mildred's. Mildred confronts Veda and is forced to admit she is a waitress. Veda treats her with derision and makes it clear that she is ashamed of her mother.
Bert arrives to take his daughters for his weekend visit. Kay contracts pneumonia on the trip and dies. Mildred channels her grief into work and throws herself into opening a new restaurant. With the help of her new friend and former supervisor, Ida (Eve Arden), Mildred's new restaurant is a success. Wally helps Mildred buy the property, and she expands into a chain of "Mildred's" throughout Southern California.
Mildred continues to smother Veda in affection and worldly goods. Veda, despite her mother's love and lavish gifts, remains spoiled, selfish, disrespectful and expresses her scorn of Mildred's common background and choice of profession. Veda's obsession with money and materialistic possessions only increases.
Veda secretly marries a well-to-do young man for his money and position, but expresses unhappiness about her marriage. Mildred and Wally agree to help her get out of the mess she's made, but Veda demands ten thousand dollars from her husband and claims she's pregnant. Her husband's family agrees, but she smugly confesses to Mildred that she lied about her pregnancy just to get the money. Mother and daughter argue, exchanging insults. Mildred tears up the check, is slapped by Veda, and throws Veda out of the house.
Bert invites Mildred out for the evening, but takes her to a club where Veda is performing as a lounge singer. Bert says he couldn't bear to tell Mildred what their daughter was doing and had to show her. Mildred begs Veda to come home, but Veda sneers and says her mother can never give her the lifestyle she wants.
Desperate to reconcile with her daughter, Mildred coaxes Monte Beragon into a loveless marriage in order to improve her social status. She knows Monte is a playboy with high social standing and an elegant mansion, but is virtually bankrupt. Monte's price for marriage is a one-third share of Mildred's business, so that he can settle his debts. Mildred agrees, and Veda, eager to live out her dream as a debutante, pretends to reconcile with her mother.
Beragon lives the life of a playboy, and takes Veda along for the ride. Mildred continues to support everyone financially, but ends up losing her business because of Monte's debts. She goes to confront Monte at his beach house, and finds her daughter in his arms. Veda scornfully tells Mildred that Monte loves her, and will leave Mildred.
Mildred runs out to her car in tears. Monte shouts that he never promised to marry Veda, and wouldn't lower himself to wed a tramp like her. A showdown ensues, and Veda shoots Monte. Mildred hears the gunshots from her car.
Veda begs her mother to help her one more time, tearfully proclaiming her love and penitence. Mildred refuses to rescue her daughter this time, and calls the police, but can't go through with it.
The detectives bring Veda into the interrogation room and explain they've trapped Mildred all along. They knew Veda committed the murder, and lead her off to jail. Mildred tells Veda "I'm sorry; I tried" but Veda, in typical careless fashion says "Don't worry about me; I'll get by" and is led away to be prosecuted. Mildred leaves the station to find Bert waiting for her.

Question: Who do detectives believe committed murder?
Answer: Veda