Fixed costs do not affect short-run marginal cost because they are just that- fixed. They are not dependent on quantity when it changes and does not vary directly with the level of output. Variable costs, however, do affect short-run marginal costs.
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When average variable costs equal to the average marginal cost, the average variable cost will be at the minimum point. i.e. lowest cost
Variable cost refers to the TOTAL variable cost of all units, whereas marginal cost is the variable cost of the last unit only. Variable cost is the sum of all the individual marginal costs. The derivative of the Variable Cost is the Marginal Cost. The integral of the Marginal cost is the Variable Cost.
It depends if the increase in Average Cost is caused by an increase in Fixed Costs or an increase in Variable Costs. An increase in Fixed Costs will not increase MC, because FCs do not vary with output (by definition) And increase in Variable Costs will increase MC
Contrast to what we would normally think, changes in fixed costs do not affect marginal cost. For example, if a product costs $10 to produce, and the fixed cost goes up to $25, then marginal cost stays the same.
When marginal productivity is diminished, the cost of productions can decrease if the marginal costs for making an extra product is larger than the marginal revenue for that 1 extra unit product.