For f(x) = x^3 - 3x^2 + 2, on which interval is the graph concave upward?
Correct answer: B. x > 1
- A. x < 1
- B. x > 1
- C. x < 0
- D. x > 0
Explanation
The second derivative is f''(x) = 6x - 6. It is positive when x > 1, so the graph is concave upward on that interval.
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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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