Here is the information I have: P(x) = 1000+$\int_{0}^{x} M(s)ds$ where P is in dollars and M is the marginal cost in dollars per unit. x is the units of products produced.
Suppose 5 units are produced a day, so then x=5t where t is in days. For writing an equation for the cost of production P as a function of time, would this work: P(5t) = 1000+$\int_{0}^{5t} M(s)ds$?
I was also asked to use the equation from above to find dP/dt. According to the fundamental theorem of calculus, would it be safe to say P'(5t) = M(5t)?