Theorems#
2007, Free Response, #3
1 |
6 |
4 |
2 |
5 |
2 |
9 |
2 |
3 |
1 |
3 |
10 |
-4 |
4 |
2 |
4 |
-1 |
3 |
6 |
7 |
The functions f and g are differentiable for all real numbers, and g is strictly increasing. The table above gives values of the functions and their first derivatives at selected values of x. The function h is given by .
Explain why there must be a value for such that .
Explain why there must be a value for such that .
2018, Free Response, #4
t (years) |
2 |
3 |
4 |
5 |
6 |
(meters) |
1.5 |
2 |
6 |
11 |
15 |
The hieght of a tree at time is given by a twice-differentiable function , where is measured in meters and is measured in years. Selected values of are given in the table above.
Use the data in the table to estimate . Using correct units, interpret the meaning of in the context of the problem.
Explain why there must be at least one time , for , such that .
2014, Free Response, #4
TODO
2014, Free Response, #5
TODO