Discussion
If \(a + b = 10\) and \(ab\) is maximum, then the value of \(a\) is
Answer: A
The value is a = 5.
Put b = 10 - a, so \(ab = a(10 - a) = 10a - a^{2}\).
\[ \frac{d}{da}(10a - a^{2}) = 10 - 2a = 0 \Rightarrow a = 5 \]
The second derivative is -2, so this is a maximum: ab = 25. That makes 25 the maximum product, not the value of a. a = 3 or 6 gives products 21 and 24, and a = 10 gives 0.
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