First it's important to determine exactly what a climax does. This is the highest point of action in the story, after which the resolution becomes clear. I would argue that the climax for the play occurs later than act 3, but since your assignment asks you to focus on this act, we'll try to determine where the conflict reaches its highest peak within these scenes.
I would argue that this happens in scene 4, when Banquo's ghost appears and sits in Macbeth's spot at the banquet. Not only does this visibly rattle Macbeth, causing him to talk to a ghost which no one else can see, but Lady Macbeth is forced to begin making excuses for her husband's behavior. When Macbeth's comments intensify, she is forced to dismiss her guests with a sense of urgency.
It is at this point that Macbeth begins to realize that perhaps getting away with murder isn't going to be as easy as he first thought. He turns his suspicions toward Macduff, who failed to appear at the banquet. Macbeth is growing in agitation and apprehension, and it is at this point that power begins to shift away from him. This is a turning point because in the scenes that follow, Macbeth is portrayed as a man who is growing increasingly desperate and unhinged.
One could argue that the climax arrives slightly later in act 3, scene 4. After Lady Macbeth has sent away all the dinner guests, Macbeth points out the fact that Macduff did not come, despite the fact that Macbeth commanded him to be there. He also says,
I am in blood
Stepped in so far that, should I wade no more,
Returning were as tedious as go o'er. (3.4.142-144)
At this point, Macbeth figures that he's already gone so far to procure the throne and, more recently, to keep it, that he might as well continue onward. He seems somewhat resigned to a bloody and violent future. He calls the idea of continuing forward "tedious," implying that he is somewhat indifferent to it; at least, he doesn't feel very strongly. Earlier, in act 3, scene 2, Macbeth seemed anything but indifferent. He said, "Oh, full of scorpions is my mind, dear wife!" (3.2.39) He even implies that it would be better to be dead than to be as anxious and tortured as he feels:
Better be with the dead,
Whom we, to gain our peace, have sent to peace,
Than on the torture of the mind to lie
In restless ecstasy. (3.2.22-25)
Macbeth felt so tortured that he almost wishes for death rather than continue on, feeling tortured. But at the end of act 3, scene 4, however, we see a turning point: Macbeth no longer feels ambivalent or pulled in two directions; he is no longer tortured about how to proceed or what to do. He seems to give in to his evil side, and this dictates his actions from here on out (actions like having the innocent Lady Macduff and her children murdered).
The climax of the play takes place in Act Three, Scene 3, when Macbeth's assassins successfully kill Banquo but are not able to murder his son, Fleance. Up to this point in the play, everything has gone the way Macbeth has planned. However, when Fleance avoids being murdered by fleeing from the assassins, Macbeth's mental stability and fortune begin to take a turn for the worse. In the next scene, the assassins tell Macbeth that Banquo is dead, but his son was able to escape. Macbeth then comments that his fears have returned and he feels uncertain about his future. Macbeth then attends a feast where he sees Banquo's ghost. Macbeth's hallucinations are a result of his guilty conscience and declining mental stability. Fleance's escape is essentially the beginning of Macbeth's downfall. From this point in the play, Macbeth's life spirals out of control, and he begins to lose his grip on reality.
In the sense of the true Elizabethan 5 Act play format, the point of conflict in act III is the point when the central character has a significant shift in power. Since Macbeth is our central character, we are looking for the point in act III that his power stops growings. This single point is most likely the killing of Banquo while Fleance escapes. It is after this point that Macbeth becomes paranoid enough to begin seeing ghosts. Although he had doubted his actions immediately after killing Duncan in act II, he still believed in the witches' prophecies until he realized that Banquo's prophecies would probably also come true.