1.

Find . (5 points)

2.

Given find f ‘(x) and give its domain. (5 points)

3.

Use a graphing calculator to graph and then select the response which is true. (5 points)

4.

Find for y = 3cos(x) + sec(x). (5 points)

5.

Differentiate . (5 points)

6.

Which one of the following statements is false? (5 points)

7.

Is the following true or false?

(5 points)

8.

If h(x) = f[g(x)], use the table of values for f, g, f ‘ and g ‘ to find the value of h ‘(1). (5 points)

x | f(x) | g(x) | f ‘(x) | g ‘(x) |
---|---|---|---|---|

1 | 3 | 2 | 2 | 6 |

2 | 1 | 8 | 5 | 7 |

3 | 7 | 2 | 7 | 9 |

9.

Determine the slope of the graph of x^{2} = ln(xy) at the point (1, e). (5 points)

10.

Find y’ if y = cos(x + y). (5 points)

Short Answer SHOW ALL WORK FOR FULL CREDIT

1.

The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours. (10 points)

a. Estimate the value of T′(6). Give units in your answer.

b. What is the meaning of T′(6)?

t | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 |
---|---|---|---|---|---|---|---|---|

T | 73 | 73 | 70 | 68 | 73 | 80 | 86 | 89 |

2.

(Find the values of m and b that make the following function differentiable.

3.

Find f ‘(x) for f(x) = cos (5x^{2}).

4.

Find f ‘(x) for f(x) = ln(x^{2} + e^{3x}).

5.

Find by implicit differentiation for x – y = xy.