1. The problem asks to list the x-values of all relative maxima and minima of the function $$C(x) = -0.1x^2 + 18x - 340$$ on the interval $$0 < x < 400$$. 2. To find relative maxima and minima, we first find critical points by setting the derivative $$C'(x)$$ equal to zero. 3. The derivative is $$C'(x) = \frac{d}{dx}(-0.1x^2 + 18x - 340) = -0.2x + 18$$. 4. Set the derivative equal to zero to find critical points: $$-0.2x + 18 = 0$$ $$-0.2x = -18$$ $$x = \frac{18}{0.2} = 90$$. 5. To determine if this critical point is a maximum or minimum, check the second derivative: $$C''(x) = \frac{d}{dx}(-0.2x + 18) = -0.2$$. 6. Since $$C''(90) = -0.2 < 0$$, the function is concave down at $$x=90$$, so this point is a relative maximum. 7. Because the parabola opens downward and there is only one critical point, there are no relative minima. 8. Therefore, the relative maximum occurs at $$x=90$$ and there are no relative minima. Final answers: - Relative maxima: $$x=90$$ - Relative minima: NONE