Would the climax of the story be when Darcy finds out the relationship that has been going on for the whole story ?

A helpful way to determine the climax of a literary work is to pinpoint the most exciting and intense point in the unfolding action. You are correct in suggesting that the climax of this book is the action-packed scene in Rachel's apartment, when Darcy spies the watch she purchased for Dex and realizes she has been betrayed. At this point in the story, the deception Rachel and Dex have spent the entire summer perpetuating is revealed, and their fear of Darcy learning the truth is realized when she reacts with extreme rage. Ironically, Darcy learns of this relationship after revealing to Rachel (and also Dex, since he can hear from the closet) that she has cheated on her fiancé with her best friend's love interest, yet she is angered by the lack of loyalty shown to her by the fiancé and best friend. Darcy then storms out of the apartment and slanders both Rachel and Dex among members of their social circle.