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Tamiku [17]
3 years ago
8

Suppose the demand for a certain item is given by:

Mathematics
1 answer:
Marysya12 [62]3 years ago
6 0

Answer:

a. D'(p) = -10p - 6

b. There is a decrease of 96 units of demand for each dollar increase

Step-by-step explanation:

The demand function is:

D(p) = - 5p^2-6p+400

(a) The derivate of the demand function with respect to price gives us the rate of change of demand:

\frac{dD(p)}{dp}=D'(p) = -10p-6

(b) When p = $9, the rate of change of demand is:

D'(9) = -10*9-6\\D'(9) = -96\ \frac{units}{\$}

This means that, when p = $9,  there is a decrease of 96 units of demand for each dollar increase.

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Step-by-step explanation:

This problem can be solved by a rule of three.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

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