1. **State the problem:** We need to find the first derivative of the function $$f(x) = x^3 - 5x + 2$$ and then evaluate it at $$x = 2$$. 2. **Find the first derivative:** Differentiate each term of $$f(x)$$: - The derivative of $$x^3$$ is $$3x^2$$. - The derivative of $$-5x$$ is $$-5$$. - The derivative of a constant $$2$$ is $$0$$. So, $$f'(x) = 3x^2 - 5$$. 3. **Evaluate the derivative at $$x = 2$$:** Substitute $$2$$ into the derivative: $$f'(2) = 3(2)^2 - 5 = 3 \times 4 - 5 = 12 - 5 = 7$$. 4. **Final answer:** The first derivative of $$x^3 - 5x + 2$$ at $$x=2$$ is $$7$$.