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practice_test.pdf

Your answer is CORRECT. Differentiate the function

a)

b)

c)

d)

e) Question 2

Your answer is CORRECT. Calculate the derivative of the given function:

a)

b)

c)

d)

e) Question 3

Your answer is CORRECT. Determine the values of x for which f '(x) = 0, given that

a)

b)

c)

d)

e) Question 4

Your answer is INCORRECT. Determine the values of x for which f '(x) < 0, given that

a) (-∞, - 2 ⁄3) ∪ (0,

2 ⁄3)

b) (- 2 ⁄3, 0) ∪ (

2 ⁄3, ∞)

c) (- 3 ⁄2, 0) ∪ (

3 ⁄2, ∞)

d) (- 3 ⁄2,

3 ⁄2)

e) (-∞, - 3 ⁄2) ∪ (0,

3 ⁄2)

Question 5

Your answer is CORRECT. Calculate the derivative of the given function:

a)

b)

c)

d)

e) Question 6

Your answer is CORRECT. Calculate the derivative of the given function:

a)

b)

c)

d)

e) Question 7

Your answer is CORRECT. Calculate the derivative of the given function:

a)

b)

c)

d)

e) Question 8

Your answer is CORRECT. Find the indicated derivative.

a)

b)

c)

d)

e) Question 9

Your answer is CORRECT. Find

dy ⁄dx .

a)

b)

c)

d)

e) Question 10

Your answer is CORRECT. Find the second derivative.

a)

b)

c)

d)

e) Question 11

Your answer is INCORRECT. Use differentials to estimate the value indicated.

a) 273

⁄50

b) 223

⁄50

c) 2

d) 124

⁄25

e) 126

⁄25 Question 12

Your answer is INCORRECT. Use differentials to estimate the value indicated.

a) 323

⁄160

b) 243

⁄160

c) 403

⁄160

d) 317

⁄160

e) 13

⁄5 Question 13

Your answer is CORRECT. Use differentials to estimate the value indicated.

a)

b)

c)

d)

e) Question 14

Your answer is CORRECT. Use one iteration of the Newton-Raphson method to estimate a root of the equation f(x) = 0 starting at the indicated value of x.

a) -7

b) 97

⁄14

c) 47

⁄7

d) 99

⁄14

e) 51

⁄7 Question 15

Your answer is CORRECT. Use one iteration of the Newton-Raphson method to estimate a root of the equation f(x) = 0 starting at the indicated value of x.

a) 7

b) -8

c) 81

⁄40

d) 79

⁄40

e) -3 Question 16

Your answer is CORRECT. The function f is graphed below on the interval [0,10].Give the number of valuesc between 0 and 10 which satisfy the conclusion of the mean value theorem for f.

a) 1

b) 5

c) 2

d) 3

e) 4 Question 17

Your answer is CORRECT. Determine if Rolles Theorem applies to the given function on [0,1]. If so, find all numbers c on the interval that satisfy the theorem.

a)

b)

c)

d)

e) Question 18

Your answer is INCORRECT. Determine if Rolles Theorem applies to the given function on [0,π]. If so, find all numbers c on the interval that satisfy the theorem.

a)

b)

c)

d)

e) Question 19

Your answer is CORRECT. Determine if the given function satisfies the Mean Value Theorem on [4,49]. If so, find all numbers c on the intervals that satisfy the theorem.

a)

b)

c)

d)

e) Question 20

Your answer is CORRECT. Determine if the given function satisfies the Mean Value Theorem on [0,2]. If so, find all numbers c on the interval that satisfy the theorem.

a)

b)

c)

d)

e)