Using the second derivative test, classify the critical points of the function f(t) = t³ - t² - t + 2 and locate any points of inflection. A) local max at t = -1/3, local min at t = 1, inflection at t = 1/3 B) local min at t = -1/3, local max at t = 1, inflection at t = 1/3 C) local max at t = 1/3, local min at t = -1, inflection at t = -1/3 D) local min at t = 1/3, local max at t = -1, inflection at t = -1/3 E) none of the above

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Quizplus · Accepted Answer

The second derivative is f''(t) = 6t - 2. f''(-1/3) < 0, so t = -1/3 is a local maximum. f''(1) > 0, so t = 1 is a local minimum. f''(1/3) = 0 and f'''(1/3) = 6 > 0, so t = 1/3 is a point of inflection.

Using the Second Derivative Test, Classify the Critical Points of the Function