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 ?

(A) The cost of painting 6 square feet is $300.
(B) The cost of painting 300 square feet is $6.
(C) The cost of painting 300 square feet is $6 per square foot.
(D) When 300 square feet have been painted, the cost to paint the next square foot is approximately $6.

Answer 1

The best interpretation of C'(300)=6 is that when 300 square feet have been painted, the cost to paint the next square foot is approximately $6.

Step-by-step explanation:

The statement C'(300)=6 means that the derivative of the cost function C(x) with respect to x, evaluated at x=300, is equal to 6. The best interpretation of this statement is (D) When 300 square feet have been painted, the cost to paint the next square foot is approximately $6.