1. Section 12.1 Techniques for Finding Derivative

2. Constant Rule Power Rule Sum and Difference Rule

3. Examples Find y’ for the function.

4. Constant Times a Function Examples: Find dy/dx for the function.

5. Marginal Functions Example: The total cost in dollars incurred each week for manufacturing q refrigerators is given by the total cost function: C(q) =8000 + 200q – 0.25q 2 What is the actual cost incurred for manufacturing the 251 st refrigerator?

6. Marginal Cost Marginal cost is the cost incurred in producing an additional unit of a certain item given that the plant is already at a certain level of operation. Mathematically, marginal cost is the rate of change of the total cost function with respect to x  derivative of the cost function. If C(x) is a total cost function, then the derivative C’(x) is called the marginal cost function.

7. Example The total cost in dollars incurred each week for manufacturing q refrigerators is given by the total cost function: C(q) =8000 + 200q – 0.25q 2 Find the marginal cost for producing 251 refrigerators.

8. Marginal Revenue / Profit If R(x) is a revenue function, then the derivative R’(x) is called the marginal revenue function. If P(x) is a profit function, then the derivative P’(x) is called the marginal profit function. Recall R(q) = pq or R(x) = px and P = R - C

9. Example The total cost C(q) =8000 + 200q – 0.25q 2 Suppose the demand equation for the refrigerators each week is given by q = 9000 – 5p. Find the marginal revenue for the production level of a) 200 units. b) 400 units.