Why ATC reaches its minimum after AVC reaches its minimum point?

Average Total Cost (ATC) reaches its minimum after Average Variable Cost (AVC) because ATC includes both AVC and Average Fixed Cost (AFC). When AVC is at its minimum, it indicates the most efficient use of variable inputs, but ATC continues to decline as AFC is spread over an increasing quantity of output. Once AVC starts to rise, the fixed costs are still being diluted, allowing ATC to decrease further until AFC no longer offsets the rising AVC. Thus, ATC reaches its minimum after AVC because it reflects both variable and fixed costs in relation to output.