Explanation:
The given function is a quadratic function with a positive leading coefficient, therefore it opens upwards and has a minimum value. To find the minimum value of the function, we can use the formula:
x = -b/2a
where a = 1 and b = 6 are the coefficients of the quadratic function.
x = -6/2(1) = -3
Substitute x = -3 into the function to find the minimum value:
f(-3) = (-3)^2 + 6(-3) + 11 = 2
Therefore, the minimum value of the function is 2.