Question

The cost, in dollars, to paint x square feet of a house is modeled by the differentiable function C(x). Which of the following is the best interpretation of the statement C'(300)=6 ?

Answer 1

The derivative C'(x) represents the rate of change of the cost function C(x) with respect to x. C'(300)=6 means that the cost of painting 300 square feet of the house is increasing at a rate of 6 dollars per additional square foot.

Step-by-step explanation:

The derivative C'(x) represents the rate of change of the cost function C(x) with respect to x. In this case, C'(300)=6 means that the cost of painting 300 square feet of the house is increasing at a rate of 6 dollars per additional square foot. This implies that for each additional square foot painted, the cost increases by 6 dollars.