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