Final answer:
The minimum value of the function f(x) = x^2 - 7x + 17.4 is -0.85.
Step-by-step explanation:
To find the minimum value of the function f(x) = x^2 - 7x + 17.4, we can start by determining the vertex of the parabola represented by the function.
The vertex of a parabola is given by the equation x = -b/2a, where a is the coefficient of x^2 and b is the coefficient of x.
In this case, a = 1 and b = -7, so the x-coordinate of the vertex is:
x = -(-7)/2(1)
= 7/2
= 3.5.
To find the minimum value, we substitute the x-coordinate of the vertex into the function to get:
f(3.5) = (3.5)^2 - 7(3.5) + 17.4
= 6.25 - 24.5 + 17.4
= -0.85.
Therefore, the minimum value of the function f(x) = x^2 - 7x + 17.4 is -0.85.