Final answer:
Without the full question details, it is not possible to accurately determine the minimum value of the function. However, for the reference function at x = 3, the option b. y = x² matches the description of having a positive slope that is decreasing with increasing x.
Step-by-step explanation:
The student asks to find the minimum value of a function for a polygonal convex set determined by a given system of inequalities. Unfortunately, the main part of the question detailing the function and the system of inequalities is missing. Therefore, based on the given information about some point coordinates, it is not possible to determine which, if any, of the listed points (3,5), (5,3), (9,7), (8,0) is the minimum of the function without additional context.
The given reference information about a function having a positive value at x=3 with a positive slope that is decreasing suggests we are considering functions whose rate of increase is reducing. Between the given options (a. y = 13x, b. y = x²), the function y = x² will have a positive value and a positive slope that decreases as x increases, which matches the described characteristics of the function f(x). Option a, y = 13x, would not have a decreasing slope; it's a constant slope.
The complete question is ....Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities.
a. The minimum is at (3,5).
b. The minimum is at (5,3).
c. The minimum is at (9,7).
d. The minimum is at (8,0)......./;