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Solve the following.
The average cost function associated with producing and marketing units of an item is given by …
The average cost function associated with producing and marketing $x$ units of an item is given by $AC = 2x - 11 + \frac{50}{x}$. Find the range of values of the output $x$, for which $AC$ is increasing.
Answer
Answer
AIDifferentiating: 2x - 11 + \frac{50}{x}
$AC = 2x - 11 + \frac{50}{x}$, with $x > 0$.
$\frac{d}{dx}(AC) = 2 - \frac{50}{x^2}$
$AC$ is increasing when $\frac{d}{dx}(AC) > 0$: $2 - \frac{50}{x^2} > 0$, so $x^2 > 25$.
Since $x > 0$, $x > 5$.
Hence $AC$ is increasing for $x > 5$.
Final answer: $2 - \frac{50}{x^2}$
From ISC 2018 Mathematics Paper 1, question 19(c).