# 10 multiple choice questions and 5 short answer questions

1.

Find . (5 points)

 2x2 + h2 + 4 2x2 + 4 4x + 4 4x

2.

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

 Domain: All real numbers, x ≠ 5. Domain: All real numbers, x ≠ 3. Domain: All real numbers, x ≠ 3, 5. Domain: All real numbers.

3.

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

 f has a horizontal tangent line f increases without bound f has no tangent line none of these responses

4.

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

 -3sin(x) + sec(x)tan(x) 3cos(x) – sec(x)tan(x) 3sin(x) – sec2(x) 3cos(x) – sec(x)

5.

Differentiate . (5 points)

 -1 -2csc(x) 2csc(x)

6.

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

 If f and g are differentiable, then . If f and g are differentiable, then . None of these statements are false.

7.

Is the following true or false?

(5 points)

 True False

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 x2 = ln(xy) at the point (1, e). (5 points)

 1 2 e e2

10.

Find y’ if y = cos(x + y). (5 points)

 0 1 -sin(x + y)

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)

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 (5x2).

4.

Find f ‘(x) for f(x) = ln(x2 + e3x).

5.

Find by implicit differentiation for x – y = xy.