# Worksheet: Estimating Derivatives

In this worksheet, we will practice using numerical and graphical methods to estimate the derivative of a function.

**Q5: **

Use the table to estimate . Take the average of the right and left derivatives.

1 | 2 | 3 | 4 | 5 | |

2.5 | 3.25 | 3.9 | 4 | 4.6 |

**Q7: **

Use the table to estimate .

2 | 5 | 6 | 8 | 9 | |

1 | 2 | 3 | 6 | 7 |

**Q9: **

The table shows the distance traveled by a car in kilometers after time in hours. Use the information shown to construct a table of values of .

Time (Hours) | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Distance (Kilometers) | 0 | 90 | 98 | 103 | 106 | 112 |

- A
Time (h) 0 1 2 3 4 5 (km/h) 90 90 8 5 3 112 - B
Time (h) 0 1 2 3 4 5 (km/h) 0 90 98 103 106 112 - C
Time (h) 0 1 2 3 4 5 (km/h) 90 98 13 8 9 12 - D
Time (h) 0 1 2 3 4 5 (km/h) 90 49 6.5 4 4.5 6 - E
Time (h) 0 1 2 3 4 5 (km/h) 90 8 5 3 112 112

**Q11: **

Use the graph of to estimate the value of .

**Q12: **

Olivia is estimating derivatives for the curve . She has drawn the following graph.

Use Oliviaβs graph to estimate .

- A3
- B
- C
- D
- E6

**Q13: **

By finding the average of the right and left approximations for the derivative, use the function table to estimate the value of .

1 | 3 | 6 | 9 | 11 | 15 | 19 | 25 | 29 | 32 | 34 | ||

7 |

- A4
- B
- C
- D6
- E5

**Q14: **

Use the function table provided to estimate the value of ).

3 | 5 | 8 | 10 | 12 | 14 | 19 | 22 | 24 | |

4 | 6 | 7 | 1 | 11 | 14 | 22 | 10 | 12 |

- A
- B
- C5
- D1
- E2

**Q15: **

Chloe and Jacob want to approximate some derivatives for the function .

Chloe draws the graph of along with tangent lines at the points where , , , and .

Jacob creates the function table for .

0 | 1 | 2 | ||

2 |

Chloe and Jacob each approximate the derivative . Chloe uses her graph, and Jacob uses his table of values. At the end points, Jacob uses right or left approximations; otherwise, he uses symmetric approximations.

State the value of each of their approximations.

- A1,
- B1,
- C1, 1
- D1,
- E,