Mathematics · Calculus

Consider the following statements regarding real-valued functions: A. A real function f(x) defined on an interval [a, b] has a maximum value in [a, b] if there exists a point c in [a, b] such that f(x) ≥ f(c) for all x ∈ [a, b]. B. A real function f(x) defined on an interval [a, b] has a minimum value in [a, b] if there exists a point c ∈ [a, b] such that f(x) ≤ f(c) for all x ∈ [a, b]. C. For f(x) = -(x - 1) 2 + 2, x ∈ R, the maximum value is 2 and the minimum value does not exist. D. For f(x) = -|x + 1| + 3, x ∈ R, the maximum value is 3 and the minimum value is 2. Which of the statements above is/are correct?