### 1 ( ) (3 3) f x x = - 40 ( ) 5 12 x f x x x =

```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
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
```