General Sternwood, the elderly millionaire father of Carmen and Vivian, initially hires Marlowe to "take care" of someone who is attempting to blackmail him. But the General's favorite hobby is taking care of his exotic orchids, so you'll usually find him in a wheelchair sitting inside his greenhouse. He may be rich, but he's not a mover and a shaker on the dark streets of L.A. He seems to be above all that.
Still, even though General Sternwood is paralyzed from the waist down, he's got some fight left in him. He and Marlowe get into some pretty heated arguments, but there are never any hard feelings between them because they develop a kind of father-son relationship.
In fact, Marlowe actually takes a shine to the General and goes out of his way to make sure he's always serving the General's best interests. Although the General never asks Marlowe to look for his son-in-law Rusty, Marlowe takes it upon himself to find out the truth, which tells us a lot both about the General and about Marlowe. For one thing, we can tell that Marlowe is pretty darn fond of the General, which is a rare sentiment for Marlowe considering his tough guy act.
And on the General's end, the fact that he doesn't want to know about Rusty's whereabouts reveals that the General is a pretty passive guy. He lets his daughters run wild, and he pays off bribes to avoid publicity. Translation: he'd rather sweep things under the rug than confront problems head on. And by the end of the novel, when Marlowe is finally able to piece together that it was the General's own daughter, Carmen, who killed Rusty, Marlowe decides to spare telling the General what would no doubt be painful news. But the General's lack of knowledge comes at a price, because it means that he will never know the full truth behind Rusty's disappearance. Then again, maybe he doesn't want to.