Please help me... I have a question from my teacher : Prove the average cost and marginal cost intersect at the minimum average cost!

The
short-run marginal cost (MC) curve will at first decline and then will go up at some
point, and will intersect the average total cost and average variable cost curves at
their minimum points.
The average variable cost (AVC) curve will go down (but
will not be as steep as the marginal cost), and then go up. This will not go up as fast
as the marginal cost curve.
The average fixed cost (AFC) curve will decline as
additional units are produced, and continue to decline.
The average total cost
(ATC) curve initially will decline as fixed costs are spread over a larger number of
units, but will go up as marginal costs increase due to the law of diminishing
returns.