# 10 multiple choice questions and 5 short answer questions

1.

Find . (5 points)

2×2 + h2 + 4

2×2 + 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)

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 (5×2).

4.

Find f ‘(x) for f(x) = ln(x2 + e3x).

5.

Find by implicit differentiation for x – y = xy.

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