Math

The cost of producing x units of a certain commodity is given by P(x)=1000+ int(MC(s))ds from 0 to x, where P is in dollars and M(x) is marginal cost in dollars per unit.
A. Suppose the marginal cost at a production level of 500 units is $10 per unit, and the cost of producing 500 units is $12,000 (that is, M(500)=10 and P(500)= 12,000). Use tangent line approximation to estimate the cost of producing only 497 units.
B. Suppose the production schedule is such that the company produces 5 units each day. That is, the number of units produced in x=5t, where t is in days, and t=0 corresponds to the beginning of production. Write an equation for the cost of production P as a function of time t.
C. Use your equation for P(t) from part B to find dP/dt. Be sure to indicate units and describe what dP/dt means, practically speaking.

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