1. **State the problem:** We need to find the equation of the tangent line to the curve defined by the function $$f(x) = 2x^3 - 9x^2 + 5x - 11$$ at the point where $$x = 2$$. 2. **Recall the formula for the tangent line:** The equation of the tangent line to the curve at $$x = a$$ is given by: $$y = f'(a)(x - a) + f(a)$$ where $$f'(a)$$ is the derivative of $$f$$ evaluated at $$x = a$$, and $$f(a)$$ is the value of the function at $$x = a$$. 3. **Find the derivative $$f'(x)$$:** $$f'(x) = \frac{d}{dx}(2x^3 - 9x^2 + 5x - 11) = 6x^2 - 18x + 5$$ 4. **Evaluate $$f'(2)$$:** $$f'(2) = 6(2)^2 - 18(2) + 5 = 6 \times 4 - 36 + 5 = 24 - 36 + 5 = -7$$ 5. **Evaluate $$f(2)$$:** $$f(2) = 2(2)^3 - 9(2)^2 + 5(2) - 11 = 2 \times 8 - 9 \times 4 + 10 - 11 = 16 - 36 + 10 - 11 = -21$$ 6. **Write the equation of the tangent line:** $$y = f'(2)(x - 2) + f(2) = -7(x - 2) - 21$$ This is the equation of the tangent line at $$x = 2$$. The problem states that simplification is not required, so this is the final answer.