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Math 148 In-Class Worksheet #4 Spring 2015 Name: 1. Sketch a graph of f (x) = 2x2 − x4 using derivative tests to find the intervals where f is increasing and decreasing, where f has relative extrema, and intervals of concavity. 2. At a certain factory, the cost of making a part is $30 per unit for labor and $10 per unit for materials. Overhead for the factor is fixed at $30,000 per week. If more than 5000 units are produced each week, and labor is $45 per unit for those units in excess of 5000, what level of production will minimize average cost? Math 148 In-Class Worksheet #4 Spring 2015 3. For a certain manufacturer, the cost function for a product is C(q) = 0.004q 3 + 20q + 5000. The demand function for the product is p(q) = 450 − 4q. How many units should be sold in order to maximize profit? p 4. The demand equation for a certain product is given by q = 3000 − p2 . (Note that here we have q in terms of p.) Find the point elasticity when p = $40. How does demand change when the price of $40 is increased by 7%? What price will maximize revenue?