C(x)=10x^2+500x+100 where as (0 is less than = x less = 15)?

Question

company manufacturing x surfsboards a day:
(a)what is the rate of chang fo total cost when the level of production is 10 surfsboard a day?

Answer 1

Just take the derivative:

C'(x) = 20x + 500
So
C'(10) = 200 + 500 = 700

Answer 2

rate of change of total cost is just the first derivative of C(x), thus C'(x)=20x+500. the rate of change of total cost when level of production is 10 surfboards is just C'(10)=700