For f(x) = x^3 - 6x^2 + 9x + 2, which critical point is a local minimum?
Correct answer: D. x = 3
- A. x = 0
- B. x = 1
- C. x = 2
- D. x = 3
Explanation
The first derivative is 3x^2 - 12x + 9, which gives critical points x = 1 and x = 3. Since f''(x) = 6x - 12 is positive at x = 3, that point is a local minimum.
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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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