Final answer:
The given function does not have a maximum value.
Step-by-step explanation:
The given function is f(x) = x² - 10x + 24.
To determine whether there is a maximum value for this function, we need to find its vertex.
The vertex of a quadratic function is given by the formula x = -b/2a. In this case, a = 1 and b = -10:
x = -(-10)/(2*1) = 5
Substituting this value back into the function, we get:
f(5) = (5)² - 10(5) + 24 = -1
Since the coefficient of x² is positive (1), the parabola opens upwards and the vertex represents a minimum point. Therefore, there is no maximum value for this function.