Math  /  Calculus

Question17 Mark for Review Aps.
Let ff be a twice-differentiable function. Which of the following statements are individually sufficient to conclude that x=2x=2 is the location of the absolute maximum of ff on the interval [5,5][-5,5] ? I. f(2)=0f^{\prime}(2)=0 II. x=2x=2 is the only critical point of ff on the interval [5,5][-5,5], and f(2)<0f^{\prime \prime}(2)<0. III. x=2x=2 is the only critical point of ff on the interval [5,5][-5,5], and f(5)<f(5)<f(2)f(-5)<f(5)<f(2). (A) II only (B) Ill only (C) I and II only
D DI and III only

Studdy Solution
Determine which statements are sufficient.
From the analysis: - Statement II is sufficient. - Statement III is sufficient. - Statement I is not sufficient.
Thus, the correct answer is (D) II and III only.
The answer is D \boxed{D} .

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