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Suppose demand for the oranges is given by the function \(q = 9 - \frac{1}{2}p\). Find the differential coefficient q'(p).

  • A.\(-\frac{1}{2}\)
  • B.\(\frac{1}{2}\)
  • C.4
  • D.9

Answer: A

The differential coefficient is \(-\frac{1}{2}\).

Differentiate the demand function with respect to price:

\[ \begin{aligned} q &= 9 - \tfrac{1}{2}p \\ q'(p) &= -\tfrac{1}{2} \end{aligned} \]

The constant 9 drops out, and the slope is negative, as the law of demand requires: quantity falls as price rises. \(\frac{1}{2}\) loses the sign, and 9 is the intercept, not the slope.

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