The cost \(C\) for producing \(x\) articles is given as \(C = x^3 - 16x^2 + 47x\). For what values of \(x\) the average cost is decreasing?Solution : Given \(C = x^3 - 16x^2 + 47x\)Average cost \(C_A = \dfrac{C}{x}\)\(\therefore C_A = \square\)Differ…

Q.3 (C)(i) The cost \(C\) for producing \(x\) articles is given as \(C = x^3 - 16x^2 + 47x\). For what values of \(x\) the average cost is decreasing?

Solution : Given \(C = x^3 - 16x^2 + 47x\)

Average cost \(C_A = \dfrac{C}{x}\)

\(\therefore C_A = \square\)

Differentiating w.r.t. \(x\), we get

\(\dfrac{d}{dx}(C_A) = \square\)

We know that \(C_A\) is decreasing if \(\dfrac{d}{dx}(C_A)\ \square\ 0\)

\(\therefore 2x - 16 \lt 0\)

\(\therefore 2x \lt 16\)

\(\therefore x \lt \square\)

\(\therefore\) Average cost is decreasing for \(x \in (0, 8)\)