Mathematics · Calculus
Consider the polynomial f(x) = x3 - 6x2 + 11x - 6 on the domain S given by 1 ≤ x ≤ 3. Let the first and second derivatives be f'(x) and f''(x) respectively. Which of the following statements is/are correct? I. The given polynomial is zero at the boundary points x = 1 and x = 3. II. There exists one local maximum of f(x) within the domain S. III. The second derivative f''(x) > 0 throughout the domain S. IV. There exists one local minimum of f(x) within the domain S.
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Only statements II and IV are correct.
- 2Only statements I and IV are correct.
- 3Only statements I, II and IV are correct.✓
- 4Only statements I, II and III are correct.
Correct answer
Only statements I, II and IV are correct.
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