Why does the average variable costs curve first rise then fall?why is it shaped like a u?
The shape of the average variable cost curve is related to the idea of diminishing marginal return. This assumes that we are talking about the short term.
In the short term, at least one of your inputs is fixed. So imagine a factory with a limited amount of machinery.
As you hire your first few workers, they use all the machines that you have. With each hire, you increase your production a lot and that makes the AVC go down because AVC = TVC/Q and when Q goes up a lot, AVC goes down.
But later, you hire more people than you have machines. When you do this, production doesn't go up as much because the extra workers can't work all the time so each worker doesn't produce as much marginal product as before. So now Q doesn't go up as much and AVC starts going back up.