Suppose that f\'(0) = 0 and f\'(3) = 0; furthermore, suppose f\'\'(0) > 0 and f\

ID: 2870428 • Letter: S

Question

Suppose that f'(0) = 0 and f'(3) = 0; furthermore, suppose f''(0) > 0 and f''(3) = 0. Which of the following statements may be deduced by applying the Second Derivative Test (SDT) by itself? A) There is a local minimum at x = 0 and local maximum at x = 3. B) The SDT is inconclusive at both X = 0 and at x = 3. C) There is a local minimum at x = 0 and SDT is inconclusive at x = 3. D) There is a local minimum at x = 0 and neither a maximum nor a minimum at x = 3. E) There is a local maximum at x = 0 and neither a maximum nor minimum at x = 3.

Explanation / Answer

I think option C is correct.

Because, f''(0)>0 then local minimum at x = 0 and f''(0) = 0 so it is inconclusive at x = 3.

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Suppose that f\'(0) = 0 and f\'(3) = 0; furthermore, suppose f\'\'(0) > 0 and f\

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