Quiz about AP Calc - IVT, EVT, MVT

Question 1

TRUE OR FALSE?  If f is continuous on [-1,1], f(-1)=4 and f(1)= -2, then there is a zero between -1 and 1.

Accepted Answer

TRUE

Answer

FALSE

Answer

CANNOT BE DETERMINED

Question 2

What is the limit?

Accepted Answer

1/4

Answer

DNE

Answer

2/3

Answer

Infinity

Question 3

Find the vertical asymptotes and holes of
y = (x+3) / (x-1)(x+3)

Accepted Answer

Holes: x = -3;
VA: x = 1

Answer

Holes: None;
VA: x = 1, -3

Answer

Holes: x = -3, 1
VA: None

Answer

Holes: x = 1
VA: x = -3

Question 4

Which of the following best describes the continuity at x = 5?

Accepted Answer

Hole

Answer

Maximum

Answer

Minimum

Answer

Vertical Asymptote

Question 5

When f'(x) changes from positive to negative, there is(are) ...

Accepted Answer

a maximum.

Answer

a minimum.

Answer

no extrema.

Question 6

When f'(x) changes from negative to positive, there is(are) ...

Accepted Answer

a minimum.

Answer

a maximum.

Answer

no extrema.

Question 7

Use the sign chart for f'(x).
There is(are) ...

Accepted Answer

no extrema.

Answer

a local maximum at x = -2.

Answer

a local maximum at x = 4.

Answer

local maxima at x = -2 and x = 4.

Question 8

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 9

Does this function have a minimum, maximum, both or neither?

Accepted Answer

Minimum

Answer

Maximum

Answer

Both

Answer

Neither

Question 10

Determine the minimum or maximum of the following function.

Accepted Answer

Max: 3

Answer

Min: -3

Answer

Max: -3

Answer

Min: 3

Question 11

Find the critical value(s) of
f(x) = x² + 2x + 1.

Accepted Answer

x = -1

Answer

x = 2

Answer

x = -1, 0

Answer

x = 0

Question 12

Find the absolute maximum value of
g(x) = 3x³ + 6x² on [-1, 1].

Accepted Answer

Abs max of 9 when x = 1, abs min of 0 when x = 0

Answer

Abs max of 8 when x = 1, abs min of -5/3 when x = -4/3

Answer

Abs max of 9 when x = 1, abs min of -5/3 when x = -4/3

Answer

Abs max of 9 when x = 1, abs min of -1 when x = -1

Question 13

How many extrema are in the picture?

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 14

If (a,b) is a local minimum of the continuous and differentiable function f, then what will be true about f'(a)?

Accepted Answer

It's zero

Answer

It's positive

Answer

It's negative

Answer

Cannot be determined

Question 15

Answer the relative minimum.

Accepted Answer

1.5

Answer

-1

Answer

0

Answer

-1 and 1.5

Question 16

Answer the relative maximum.

Accepted Answer

-1 and 1.5

Answer

-1

Answer

0

Answer

1.5

Question 17

What is the average rate of change of the function below over the indicated interval?
f(x) = x² - 3x - 28, [-4,7]

Accepted Answer

0

Answer

11

Answer

6

Answer

66

Question 18

At what x-value(s) does f(x) have a minimum? (Be careful this is a graph of f'!)

Accepted Answer

x = 5

Answer

x = -3

Answer

x = 1

Answer

x = -3 and x = 5

Question 19

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

Accepted Answer

It's negative

Answer

It's positive

Answer

It's zero

Answer

Cannot be determined

Question 20

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 21

The concavity of a function is described by its _______________.

Accepted Answer

second derivative

Answer

first derivative

Answer

third derivative

Answer

expression

Question 22

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

Accepted Answer

concave down

Answer

increasing

Answer

decreasing

Answer

concave up

Question 23

Identify the interval from the derivative graph where the function is concave down

Accepted Answer

(-3,-1) & (1,3)

Answer

(-1,1) & (3,4)

Answer

(-2,4)

Answer

(-2,1) & (1,4)

Question 24

Identify the interval from the derivative graph where the function is concave up.

Accepted Answer

(-1,1) & (3,4)

Answer

(-3,-2)

Answer

(-2,-1)

Answer

(-3,-1) & (1,3)

Question 25

Given the following graph of f', the derivative of f. For what x-value does f have a relative minimum?

Accepted Answer

x=-3

Answer

x=-1 and x=4

Answer

x=1

Answer

x=3

Question 26

Find the x-coordinate of the inflection point of f(x)=6x²-x³.

Accepted Answer

2

Answer

-2

Answer

0

Answer

None

Question 27

Find where f(x)=6x²-x³ is concave up.

Accepted Answer

x<2

Answer

x>2

Answer

x< -2

Answer

x> -2

Question 28

Find where f(x)=6x²-x³ is decreasing.

Accepted Answer

x<0 or x>4

Answer

(-4,0)

Answer

(0,4)

Answer

x<-4 or x>0

Question 29

Find the x-coordinate of the relative max of f(x) = 6x²- x³

Accepted Answer

4

Answer

-4

Answer

0

Answer

None

Question 30

The function has an absolute minimum.

Accepted Answer

False

Answer

True

Question 31

The function has an relative maximum.

Accepted Answer

True

Answer

False

Question 32

Which of the following best describes the continuity at x = 5?

Accepted Answer

Infinite Discontinuity

Answer

Continuous

Answer

Removable Point Discontinuity

Answer

Jump Discontinuity

Question 33

Assume this is a graph of f. What can you say about its first and second derivative from x=1 to x=5?

Accepted Answer

f'(x) < 0 and f''(x) > 0

Answer

f'(x) > 0 and f''(x) > 0

Answer

f'(x) < 0 and f''(x) < 0

Answer

f'(x) > 0 and f''(x) < 0

Question 34

How many horizontal tangents would p(x) have?

Accepted Answer

3

Answer

2

Answer

1

Answer

4

AP Calc - IVT, EVT, MVT

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