Final answer:
For the function f(x) = 1/x on the interval (1, \infty), there is no absolute maximum value and the minimum value is at x = 1. This corresponds to choice a.
Step-by-step explanation:
The function f(x) = \frac{1}{x} is defined for all real numbers except x = 0. On the interval (1, \infty), we are asked to find the absolute maximum and minimum values attained by this function. According to the properties of the function, as x approaches infinity, f(x) approaches 0. However, f(x) never actually reaches 0, implying that there is no absolute minimum value on the interval (1, \infty). On the other end, as x approaches 1 from the right, f(x) approaches 1, which is the highest value f(x) attains on this interval. Hence, the absolute maximum occurs at x = 1.
So, the correct answer to the question is: The function has no absolute maximum, and the minimum value is at x = 1, which corresponds to choice a. No maximum, minimum at (x = 1).