Question

Let f be a function such that f(2) ≤ f(x) for all values of x in the interval (0, 3). Does f(2) represent a relative minimum or a relative maximum?

Answer 1

Answer: f(2) is a relative minimum

This is because f(2) is the lowest y output for any given y = f(x) output on the interval $0 < x < 3$ which is what the interval notation (0,3) indicates.

Draw out a "parabolic" like shape where the lowest point occurs at (2, f(2)), where f(2) is unknown, but we at least know that x = 2. I put "parabolic" in quotes because it may not be a true parabola, but it looks like one. This lowest point only applies for the neighbor hood $0 < x < 3$.