To solve the problem, we start by analyzing the given condition for the quadratic function (f(x) = ax^2 + bx + c):
For a quadratic function, if (f(m) = f(n)), the axis of symmetry is the midpoint of (m) and (n):
[x = \frac{m + n}{2}]
Given (f(4) = f(1)), the axis of symmetry is:
[x = \frac{4 + 1}{2} = 2.5]
Points (x=2) and (x=3) are equidistant from the axis of symmetry ((2.5 - 2 = 0.5) and (3 - 2.5 = 0.5)).
Quadratic functions are symmetric about their axis of symmetry, so values at equidistant points are equal.
Answer: (f(2) = f(3))
(\boxed{f(2)=f(3)}) (or if the question expects a numerical relationship, but likely the equality is the answer. Depending on formatting, maybe just state they are equal, but in boxed form as per convention: (\boxed{f(2)=f(3)}))
But if the question asks which is larger, the answer is they are equal. So final answer is (\boxed{f(2)=f(3)}) (or simplified to (\boxed{=}) if needed, but probably the equality statement is expected).
Wait, maybe the original question was asking to compare, so the answer is that (f(2)) equals (f(3)), so the boxed answer could be (\boxed{f(2)=f(3)}) or just (\boxed{=}) but more likely the equality.
Alternatively, if the options were given, but based on the problem, the conclusion is (f(2)=f(3)).
Final Answer: (\boxed{f(2)=f(3)})
But sometimes in such problems, they might expect a symbol, so (\boxed{=}) is also possible. However, the most precise is (\boxed{f(2)=f(3)}).
(\boxed{f(2)=f(3)})
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