A rectangle has a perimeter of 40 cm. What is its maximum possible area?
Correct answer: C. 100 cm²
- A. 80 cm²
- B. 90 cm²
- C. 100 cm²
- D. 120 cm²
Explanation
If the sides are x and 20 - x, the area is A = x(20 - x). This quadratic is maximised at x = 10, giving a square with area 10 × 10 = 100 cm².
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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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