Quiz about Calculus 1st Semester Review

Question 1

Where is the graph continuous yet NOT differentiable?

Accepted Answer

x = b, d

Answer

x = a, b, c, d

Answer

x = b, c, d

Answer

x = a, b,

Question 2

Find h'(3)

Accepted Answer

1

Answer

-2

Answer

0

Answer

3

Question 3

What is the limit?

Accepted Answer

17/3

Answer

5/2

Answer

-2/3

Answer

Infinity

Question 4

What is the limit?

Accepted Answer

12

Answer

DNE

Answer

Infinity

Answer

6

Question 5

Question 5.

Accepted Answer

1/2

Answer

0

Answer

Positive Infinity

Answer

Negative Infinity

Question 6

Question 6.

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 7

Question 7.

Accepted Answer

[-2,3]

Answer

[-2,1]

Answer

[3,5]

Answer

[0,1.5] and [3,5]

Question 8

Question 8.

Accepted Answer

I and II Only

Answer

I only

Answer

I, II, and III

Answer

II Only

Question 9

Find f'(x)

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 10

A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction?

Accepted Answer

6.5

Answer

2

Answer

4

Answer

7

Question 11

Question 11.

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 12

Find dy/dx

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 13

If A = 2x³, what is (dA/dt)?

Accepted Answer

6x²(dx/dt)

Answer

6x2

Answer

6x²(dA/dx)

Answer

6x (dx/dt)

Question 14

Given a graph of f'', which could be a Point of Inflection?

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 15

f' is given, which could be f?

Accepted Answer

C

Answer

A

Answer

B

Question 16

What is true about the following?

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 17

Where is the graph not differentiable?

Accepted Answer

x = -2, -1, 1

Answer

x = -2, -1, 0, 1

Answer

x = -2, -1

Answer

x = -1,

Question 18

Question 18.

Accepted Answer

0 < t < 2

Answer

1 < t < 5

Answer

2 < t < 6

Answer

3 < t < 5

Question 19

Find the second derivative of f(x) = x²+ e^x - cosx

Accepted Answer

f"(x) = 2 + e^x + cosx

Answer

f"(x) = 2x + e^x + cosx

Answer

f"(x) = 2x + xe^x - cosx

Answer

f"(x) = 2x + e^x + sinx

Question 20

Question 20.

Accepted Answer

Average Rate of Change

Answer

Average Value of f

Answer

Intermediate Value Theorem

Answer

Rolle's Theorem

Question 21

Question 21.

Accepted Answer

velocity

Answer

position

Answer

acceleration

Answer

total distance

Question 22

Which of the following are synonyms for find the derivative?

Accepted Answer

f'(x)

Accepted Answer

dy/dx

Accepted Answer

y'

Accepted Answer

slope of the tangent line

Accepted Answer

instantaneous rate of change

Question 23

Given u(x) = f(x)g(x), f(2) = 3, g(2) = -3, f '(2) = 5, and g'(2) = 1,

then u'(2) = ?

Accepted Answer

-12

Answer

4

Answer

5

Answer

12

Question 24

If f has a derivative at x = a, then f is continuous at x = a?

Accepted Answer

True

Answer

False

Question 25

The function f has positive 1st derivatives and a negative 2nd derivative. Which of the following could be a table of values for f ?

Accepted Answer

B

Answer

A

Answer

C

Question 26

Which is true at a?

Accepted Answer

f'(a) < f(a) < f''(a)

Answer

f'(a) < f''(a) < f(a)

Answer

f''(a) < f'(a) < f(a)

Answer

f'(a) = f''(a) < f(a)

Question 27

Where does f(x) have a point of inflection?

Accepted Answer

x = -1,3

Answer

x = -3

Answer

x = 3,-3

Answer

x= -1

Question 28

A particle's speed is decreasing if

Accepted Answer

it's velocity and acceleration have different signs

Answer

it's acceleration is positive

Answer

it's velocity is positive

Answer

it's velocity and acceleration have the same sign

Question 29

An objects distance from its starting point at time t is given by the equation

s(t) = t³ - 6t² - 4.

What is the speed of the object when its acceleration is 0?

Accepted Answer

12

Answer

2

Answer

-24

Answer

44

Question 30

Use the sign chart for f'(x) and the table of f(x).  There is ...

Accepted Answer

all of the above

Answer

a local maximum at (-10,5).

Answer

an absolute minimum at (-2,0).

Answer

a local minimum at (20,7).

Question 31

If H(x) = f ^-1(x), then H'(3) equals

Accepted Answer

1/4

Answer

4

Answer

- 1/4

Answer

-4

Question 32

Find dy/dx at a given point.

Accepted Answer

5/4

Answer

4/5

Answer

1

Answer

-5

Question 33

Find the derivative of the inverse

Accepted Answer

1/12

Answer

12

Answer

146

Answer

1/146

Question 34

find y'

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 35

Find the Derivative

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 36

Question 36.

Accepted Answer

The Quotient and Chain Rules

Answer

Only the Quotient Rule

Answer

The Quotient and Product Rules

Answer

Only the Chain Rule

Question 37

Find all values of c that satisfy the MVT for the function on the given interval

f(x) = -x² + 8x - 17 on [2,6]

Accepted Answer

c = 4

Answer

c = 2

Answer

c = 3

Answer

c = 6

Question 38

A hypothetical cube shrinks so that the length of its sides are decreasing at a rate of 4 m/min. At what rate is the volume of the cube changing when the sides are 5 m each?

Accepted Answer

-300 m³/min

Answer

-296 m³/min

Answer

-297 m³/min

Answer

-307 m³/min

Question 39

If (a,b) is a local minimum, then what will be true about f''(a)?

Accepted Answer

It's postive

Answer

It's negative

Answer

It's zero

Answer

Cannot be determined

Question 40

If f''(x)>0 over the interval (-7,1), then what will be true about f'(x)?

Accepted Answer

It's increasing

Answer

It's constant

Answer

It's decreasing

Answer

Cannot be determined

Question 41

Question 41.

Accepted Answer

Mean value theorem

Answer

Instantaneous Rate of Change

Answer

Intermediate Value Theorem

Answer

Fundamental Theorem of Calculus

Question 42

Based on the table, use LRAM and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

Accepted Answer

5(3) + 1(4) + 2(5) + 1(7)

Answer

5(4) + 1(5) + 2(7) + 1(6)

Answer

5(3) + 6(4) + 8(5) + 9(7)

Answer

0(3) + 5(4) + 6(5) + 8(7)

Question 43

True/False: if the limit of a function exists at x=c, then f(c) exists.

Accepted Answer

False

Answer

True

Question 44

If f(x) is continuous at interval [a,b], and f(a) is positive and f(b) is negative, then f(c)=0, where c is include in [a,b].

Accepted Answer

True

Answer

False

Question 45

Find the limit as x approaches -3

Accepted Answer

-6

Answer

0

Answer

1

Answer

DNE

Question 46

List the horizontal and vertical asymptotes of the function.

Accepted Answer

y = -2

Accepted Answer

x = -3

Accepted Answer

x = 3

Answer

y = 2

Question 47

Question 47.

Accepted Answer

DNE

Answer

0

Answer

1

Answer

-1

Question 48

Question 48.

Accepted Answer

-1

Answer

5

Answer

infinity

Answer

1

Question 49

Find the value of f so that f(x) is continuous at x = -1

Accepted Answer

-3

Answer

3

Answer

1

Answer

-1

Question 50

Find the second derivative of
f(x) = x²+ e^x - cosx

Accepted Answer

f"(x) = 2 + e^x + cosx

Answer

f"(x) = 2x + e^x + cosx

Answer

f"(x) = 2x + xe^x - cosx

Answer

f"(x) = 2x + e^x + sinx

Question 51

Find the Limit

Accepted Answer

8x

Answer

4x2-3

Answer

4x+4h-3

Answer

4x

Question 52

Question 52.

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 53

Question 53.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 54

Question 54.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 55

What is x-value at which the function below has the same instantaneous rate of change as the average rate of change over the indicated interval?

f(x) = x² - 3x - 28, [-4,7]

Accepted Answer

1.5

Answer

-1.5

Answer

0.5

Answer

-0.5

Question 56

In order for the Extreme Value theorem to apply, which of these must be true. Select all that apply.

Accepted Answer

It must be continuous

Accepted Answer

It must be closed

Answer

It must be discontinuous

Answer

It must be open

Question 57

Question 57.

Accepted Answer

5/3

Answer

0

Answer

e5x

Answer

DNE

Question 58

The following is a description of what theorem?

If a function is differentiable, then the derivative must be equal to the Average Rate of Change somewhere on that interval.

Accepted Answer

Mean Value Theorem

Answer

Intermediate Value Theorem

Answer

Exteme Value Theorem

Answer

Differentiable Value Theorem

Question 59

The following is a description of what theorem?

If a function is continuous, then it is guaranteed to get every y value in between the endpoints on an interval.

Accepted Answer

Intermediate Value Theorem

Answer

Mean Value Theorem

Answer

Exteme Value Theorem

Answer

Differentiable Value Theorem

Question 60

The following is a description of what theorem?

If you have a closed, continuous interval, there MUST be an absolute max and min.

Accepted Answer

Exteme Value Theorem

Answer

Intermediate Value Theorem

Answer

Mean Value Theorem

Answer

Differentiable Value Theorem

Question 61

If asked to find the absolute maximum of a function and then JUSTIFY, what is the best way to justify on a free response question?

Accepted Answer

A table including end points and critical points, and the values you get when you plug into the function

Answer

A table including just critical points and the values you get when you plug into the function

Answer

A sign chart including just critical points to determine all of the maxes.

Answer

A sign chart including critical points and end points to determine all of the maxes.

Calculus 1st Semester Review

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