A square sheet has side length 12 cm. Equal squares of side x are cut from its four corners and the sides are folded to form an open box. Which value of x gives the maximum volume?
Correct answer: B. 2 cm
- A. 1 cm
- B. 2 cm
- C. 3 cm
- D. 4 cm
Explanation
The volume is V(x) = x(12 - 2x)². Differentiating gives critical values x = 2 and x = 6, but x = 6 produces zero volume, so the maximum occurs at x = 2 cm.
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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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