Final answer:
The maximum function value of p(x) will correspond to the minimum value of f(x) due to the negation relationship p(x) = -f(x). The maximum value of p(x) and its location cannot be specified without further details about f(x), but it's typically at an endpoint of the f(x) domain.
Step-by-step explanation:
To find the maximum function value of p(x), we need to consider the function f(x) that p(x) is based on. Since p(x) = -f(x) and we know that f(x) has a maximum value of m when x = 0, then p(x) will have a minimum value at the same x-value. This is because negating the function f(x) inverts its graph, turning maximum points into minimum points and vice versa.
That being said, if the original function f(x) has a maximum value of m = 0.25 at x = 0, then p(x) will have a minimum value of -m = -0.25. To find the maximum value of p(x), we need to look at the minimum value of f(x). If the graph of f(x) is a declining curve, its minimum would occur at the highest x-value in the domain of f(x). Without more information about f(x), we cannot specify the exact x-value or the maximum of p(x). Assuming that the minimum of f(x) is at the endpoint of its domain, say x = a, then the maximum of p(x) would be at that same x = a, with a value of p(a) = -f(a).