Answer:
The minimum value of the function is ƒ(3) = 5.
Explanation:
To find the minimum value of ƒ(x), we need to find the vertex of the parabola represented by the function. We can do this by completing the square:
ƒ(x) = x² - 6x + 14
ƒ(x) = (x - 3)² - 9 + 14 (adding and subtracting the square of half the x coefficient, which is -3)
ƒ(x) = (x - 3)² + 5
The vertex of the parabola is at (3, 5), and since the coefficient of the squared term is positive, the parabola opens upward. Therefore, the minimum value of the function is ƒ(3) = 5.