Question

Derivative of Average cost \((AC)=5+\frac{2}{Q}\) is:

• A. \(-\frac{2}{Q^2}\)
• B. \(\frac{2}{Q^2}\)
• C. \(\frac{2}{Q}\)
• D. \(\frac{1}{Q}\)

Hint:

Convert fractions into powers before differentiating: \(\frac{1}{Q}=Q^{-1}\). Then use \(\frac{d}{dQ}(Q^n)=nQ^{n-1}\).

Answer 1

The Correct Option is A

Concept: Derivative measures the rate of change of a function. Here, we have to differentiate the average cost function with respect to \(Q\). \[ AC=5+\frac{2}{Q} \]

Step 1: Rewrite the function using power form.
\[ AC=5+2Q^{-1} \]

Step 2: Differentiate each term with respect to \(Q\).
\[ \frac{d}{dQ}(5)=0 \] and \[ \frac{d}{dQ}(2Q^{-1})=2(-1)Q^{-2} \]

Step 3: Simplify the derivative.
\[ \frac{d(AC)}{dQ}=-2Q^{-2} \] \[ \frac{d(AC)}{dQ}=-\frac{2}{Q^2} \] Therefore, the correct answer is option (A).