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Flashcards in Chapter 8 Test Deck (20)
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1
Q

Below is a graph on which four points have been labeled. At which of the points does the tangent line not exist?

A

Point B

2
Q

Below is a graph which has been divided into four sections. In which of these sections is the derivative of the function always negative?

A

Section D

3
Q

Below is a graph on which four points have been labeled. At which of them is the slope of the tangent line negative?

A

Point C

4
Q

Below are four tables with points from y = f (x) listed. Which of the tables could belong to a function that is symmetric around the y-axis?

A
x  y
0 -2
1  14
2  -2
-1  14
-2  -2
5
Q

The function f (x) = 2x^ 3 − 21x ^2 + 72x − 49 has critical points at x = 3 and x = 4. Which sign chart describes these critical points?

A

-

6
Q

What are the critical points of the function f(x) = x+1/x?

A

x = −1, 1

7
Q

What is the maximum value that f (x) = x^ 3 − 3x ^2 + 3x + 9 attains?

A

This function has no maximum.

8
Q

The function f (x) = x^ 3 − 6x ^2 + 12x + 10 has a critical point that is neither a maximum nor a minimum. What are its coordinates?

A

(2, 18)

9
Q

How many points of inflection are there for the graph of f(x)= −3x^5+5x^3?

A

3

10
Q

On which of the following intervals is the graph of

f(x) = x^2+1/x^2−4 concave down?

A

(−2,2)

11
Q

What are the x-coordinates of the points of inflection of f(x)=x(x−4)^3?

A

x=2 and x=4

12
Q

If the graph of the second derivative is shown, on which of the following intervals is f(x) concave down?

A

(s, t)

13
Q

The graph of f(x) is shown. Which of the following intervals has both f′(x)>0 and f′′(x)<0 ?

A

(q, r)

14
Q

If the graph of the derivative of f (x) is shown, at which x-coordinates would f (x) have a point of inflection?

A

x = q only

15
Q

If the graph of the derivative of f (x) is shown, on which intervals would f (x) be concave down?

A

(q, r)

16
Q

On which interval is f (x) = 3x^ 5 − 20x ^3 increasing?

A

(−∞,−2) and (2, ∞)

17
Q

Which of the following equations could be an equation of a vertical asymptote of y=x^2+2x−3/√x

A

x=0

18
Q

Which of the following equations has no vertical asymptote?

A

x/x^2 + 2x+ 7

19
Q

Which equation is represented by the following graph?

A

y=(x+1)^2/x

20
Q

Which of the following represents the graph of y=2x−1/x+1?

A

-

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