A company produces x units with cost function: C(x) = 2x2 − 12x + 50. Find the production level that minimizes cost.

The given cost function is $C(x) = 2x^2 - 12x + 50$.

$$C'(x) = \frac{d}{dx}(2x^2 - 12x + 50)$$ $$C'(x) = 4x - 12$$

To find the critical point where the cost is minimized, we set $C'(x) = 0$:

$$4x - 12 = 0$$ $$4x = 12$$ $$x = \frac{12}{4}$$ $$x = 3$$

Find the second derivative of $C(x)$:

$$C''(x) = \frac{d}{dx}(4x - 12)$$ $$C''(x) = 4$$

Since $C''(x) = 4 > 0$, the cost function has a local minimum at $x=3$.

The production level that minimizes cost is 3 units.

$$3 \text{ units}$$