Use the demand function $x = 250 \left( 1 - \frac { 5 p } { 7 p + 2 } \right)$ to find the rate of change in the demand x for the given price $p = \$ 2.00$ . Round your answer to two decimal places.
A)9.77 units per dollar
B)-1.95 units per dollar
C)1.95 units per dollar
D)3.47 units per dollar
E)-9.77 units per dollar

Question

Quizplus · Accepted Answer

To find the rate of change of demand with respect to price, differentiate the demand function with respect to $p$, then evaluate at $p = 2$. The derivative is $-\frac{250 \cdot 35}{(7p + 2)^2}$. Substituting $p = 2$ gives $-9.77$ units per dollar.

Use the Demand Function x=250(1−5p7p+2)x = 250 \left( 1 - \frac { 5 p } { 7 p + 2 } \right)x=250(1−7p+25p​)

Use the Demand Function $x = 250 \left( 1 - \frac { 5 p } { 7 p + 2 } \right)$