If f'(1) = 0 and f''(1) = 0, what conclusion follows from the second derivative test?
Correct answer: C. The test gives no definite classification
- A. A local maximum is certain
- B. A local minimum is certain
- C. The test gives no definite classification
- D. An inflection point is certain
Explanation
When the second derivative is zero at a stationary point, the second derivative test is inconclusive. Further analysis, such as checking the sign of f'(x), is required.
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About Differentiation and Optimisation
Differentiation covers gradients, standard derivative rules, the product and quotient rules, the chain rule, stationary points and rates of change. Optimisation uses first and second derivatives to classify maxima and minima, while applications include tangent and normal lines, marginal quantities and related rates.
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