Math 19 Practice Problems Fall 2014 1. Find the slope of the tangent line to the curve f ( x) 1 when x = 2. (3x 3)3 2. Find the slope of the tangent line to the curve f ( x) 40 x3 2 when x = -2 5 x x4 12 3. Find the equation of the tangent line to the curve f ( x) 4 x 2 5 when x = 3. 4. For what values of x will the slope of the tangent line to the curve f ( x) 5(5 2 x)2 be 8? 5. Find the values of x where the tangent line to the curve f ( x) x2 is horizontal. 3x 4 6. The profit made from selling packages of Mickey’s Macaroons is given by P( x) .01x3 .2 x 2 24 x 20 dollars for x packages. Find the marginal profit on 10 packages. 7. The cost to make a dozen of Sally’s Super Snickerdoodles is given by C ( x) 2 x(2 x) 2 dollars for x dozen cookies. Find the marginal cost to make 5 dozen cookies. 8. The postion of a toy car t seconds after it is released is given by s(t ) 16t 2 12t 10 feet. Find the velocity after 10 seconds. 9. At the Audubon Center the number of bluebirds in residence has increased due to a number of bluebird boxes installed in the woods around the center. The population can be described by N (t ) 0.2 x 2 20 x 100 birds, t years after the boxes were installed. a. Find the average rate of change in the bluebird population between 4 and 6 years after the boxes were installed. b. Find the (instantaneous) rate of change in the bluebird population 4 years after the boxes were installed. KEY 1. Slope = -1/9 2. Slope = 26 3. y = 6x – 10 4. x = 108/40 = 2.7 5. x = 0, 8/3 6. Marginal Profit is $23/package 7. Marginal Cost $238/dozen 8. velocity is 332 feet/second 9. a. Average rate of change is 22 bluebirds/year b. Instantaneous rate of change (derivative) is 21.6 bluebirds/year

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