## Practice Problems

Work through the odd-numbered problems 1-17. Once you have completed the problem set, check your answers.

1. Use the function in Fig. 12 to fill in the table and then graph .

= the estimated slope of the tangent line to at the point (x,y) | ||
---|---|---|

0 | ||

0.5 | ||

1.0 | ||

1.5 | ||

2.0 | ||

2.5 | ||

3.0 | ||

3.5 | ||

4.0 |

3.

(a) At what values of does the graph of f in Fig. 14 have a horizontal tangent line?

(b) At what value(s) of is the value of f the largest? smallest?

(c) Sketch the graph of = the slope of the line tangent to the graph of at the point .

5.

(b) Sketch the graph of = slope of the line tangent to the graph of at the point .

(c) Your graph in part (b) should look familiar. What function is it?

Problems 7 – 9 assume that a rocket is following the path , from left to right.

7. At what point should the engine be turned off in order to coast along the tangent line to a base at ?

9. At what point should the engine be turned off in order to coast along the tangent line to a base at ?

For each function in problems 11-15, perform steps :

In problem 17, use the result that if then .

17. At which point(s) does the line tangent to the graph at that point also go through the point ?

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-3.1-Introduction-to-Derivatives.pdf

This work is licensed under a Creative Commons Attribution 3.0 License.