Question

Suppose the demand for a certain item is given by D(p)=−2p2−6p+300, where p represents the price of the item in dollars:

a. Find the rate of change of demand with respect to price

Answer 1

The rate of change of demand concerning price for the function D(p) = −2p2 −6p + 300 is computed by differentiating the function, yielding D'(p) = -4p - 6.

Step-by-step explanation:

The rate of change of demand with respect to price for the given demand function D(p) = −2p2 −6p + 300 is found by computing the derivative of D with respect to p. This represents the slope of the demand curve at a given point and is mathematically represented as D'(p).

To find this rate of change, we differentiate the demand function:

D'(p) = d/dp (-2p2 - 6p + 300)

Applying the power rule, we get:

D'(p) = -4p - 6

Therefore, the rate of change of demand with respect to price is -4p - 6. This indicates how demand varies as the price changes; specifically, for every unit increase in price, the demand decreases by 4 units plus an additional 6.