1. **State the problem:** Find the coordinates of the point of inflection of the function $f(x) = x^3 - 3x + 2$. 2. **Recall the formula and rules:** The point of inflection occurs where the second derivative $f''(x)$ changes sign, which means $f''(x) = 0$. 3. **Find the first derivative:** $$f'(x) = \frac{d}{dx}(x^3 - 3x + 2) = 3x^2 - 3$$ 4. **Find the second derivative:** $$f''(x) = \frac{d}{dx}(3x^2 - 3) = 6x$$ 5. **Set the second derivative equal to zero to find possible inflection points:** $$6x = 0 \implies x = 0$$ 6. **Find the corresponding $y$-coordinate:** $$f(0) = 0^3 - 3(0) + 2 = 2$$ 7. **Conclusion:** The point of inflection is at $(0, 2)$. **Answer:** C. $(0, 2)$