Final answer:
The minimum value of the function f(x) = x² + 6x + 11 is 11.
Step-by-step explanation:
To find the minimum value of the function f(x) = x² + 6x + 11, we can use the concept of completing the square. First, rewrite the function in the form (x + a)² + b. In this case, a = 3 and b = 2. To find the minimum value, we set x + a = 0, which gives x = -a. Substituting this value back into the function, we find that the minimum value is (3)² + 2 = 11.