Introduction:
In microeconomics, cost curves are graphical representations of the relationship between the quantity of output produced and the cost of production. They help firms analyze and make decisions about production levels and pricing strategies. There are various types of cost curves, including the average cost curve, marginal cost curve, average variable cost curve, and average fixed cost curve.

Explanation:
Among the given options, the cost curve that is never U-shaped is the average fixed cost curve. To understand why, let's look at each of the cost curves individually:

1. Average cost curve:
- The average cost curve is obtained by dividing the total cost by the quantity of output.
- It is U-shaped because initially, as output increases, the fixed costs are spread over a larger quantity of output, leading to a decrease in average cost.
- However, beyond a certain point, the average cost starts increasing due to diminishing returns to scale or other factors.
- Therefore, the average cost curve is U-shaped.

2. Marginal cost curve:
- The marginal cost curve represents the additional cost incurred to produce one more unit of output.
- It is U-shaped because at lower levels of output, firms can benefit from economies of scale and specialization, leading to a decrease in marginal cost.
- However, as the firm reaches its optimal production level, the law of diminishing returns sets in, and marginal cost starts rising.
- Therefore, the marginal cost curve is U-shaped.

3. Average variable cost curve:
- The average variable cost curve represents the variable cost per unit of output.
- It is U-shaped because initially, as output increases, the fixed costs are spread over a larger quantity of output, leading to a decrease in average variable cost.
- However, as the law of diminishing returns sets in, the average variable cost starts rising.
- Therefore, the average variable cost curve is U-shaped.

4. Average fixed cost curve:
- The average fixed cost curve represents the fixed cost per unit of output.
- Unlike the other cost curves, the average fixed cost curve is always downward sloping and never U-shaped.
- This is because fixed costs do not change with changes in the quantity of output.
- As the quantity of output increases, the fixed costs are spread over a larger quantity of output, resulting in a decrease in average fixed cost.
- Therefore, the average fixed cost curve is downward sloping.

Conclusion:
Among the given options, the cost curve that is never U-shaped is the average fixed cost curve. This is because fixed costs do not change with changes in the quantity of output, resulting in a downward-sloping curve as the quantity of output increases.