**1. **Application of Differentiation

**2. **Derivatives of Logarithmic Functions Find dy/dx
1.
2.
3.
4.

**3. **Derivatives of Exponential Functions Find dy/dx
1.
2.
3.

**4. **Applied Maxima and Minima Maximizing Revenue
Minimizing Average Cost
Profit Maximization
Elasticity of Demand

**5. **Maximizing Revenue 1. The demand equation for a manufacturer?s product is p = 20 - 0.25q, 0 ? q ? 80
where q is the number of units and p is the price per unit. At what value of q will there be maximum revenue? What is the maximum revenue?
2.The demand equation for a monopolist?s product is p = -5q + 30. At what price will revenue be maximized?

**6. **Minimizing Average Cost 1.A manufacturer?s total cost function is given by c = q2/4 + 3q + 400
where c is the total cost of producing q units. At what level of output will average cost per unit be a minimum?
2.A manufacturer finds that the total cost c of producing a product is given by the cost function c = 0.05q2 + 5q + 500
At what level of output will average cost per unit be a minimum?

**7. **TUGAS 1. For Monopolist?s product, the demand function is p = 72 - 0.04q and the cost function is c = 500 + 30q. At what level of output will profit be maximized? At what price does this occur, and what is the profit?
2. For a monopolist?s product, the demand equation is p = 42 - 4q, and the average cost function is = 2 + 80/q. Find the profit maximizing price

**8. **Profit Maximization 3. Suppose that the demand equation for a monopolist?s product is p = 400 - 2q and the average cost function is = 0.2q+4+400/q, where q is number of units and both p and
are expressed in dollars per unit
a.Determine the level of output at which profit is maximized
b.Determine the price at which maximum profit occurs
c.Determine the maximum profit

**9. **Elasticity of Demand Economists measure how a change in the price of a product will affect the quantity demanded
The ratio of the resulting percentage change in quantity demanded to a given percentage change in price:
% change in quantity
% change in price

**10. **Continue ?... If p = f(q) is a differentiable demand function, the point elasticity of demand denoted by:

**11. **Continue ?... 1. When |?| > 1, demand is elastic
2. When |?| = 1, demand has unit elasticity
3. When |?| < 1, demand is inelastic

**12. **Continue ?... Example 1
a. Find the point elasticity of demand for the demand function p = 1200 - q2 at q = 10.
b. Determine the point elasticity of demand equation q = p2 - 40p + 400 (where q > 0) at p = 15.

**13. **Elasticity and Revenue

**14. **Continue ?... If demand is elastic, then ? < -1,
so 1 + 1/ ? > 0
? total revenue increases if demand elastic
If demand is inelastic, then ? > -1,
so 1 + 1/ ? < 0
? total revenue decreases if demand
inelastic