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Chapter 8 Practice Test Flashcards

(20 cards)

1
Q

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

A

Point B

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2
Q

Below is the graph of a function on which four points have been labeled. Which of the following statements about these points is true?

A

The derivative of the function at point B does not exist

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3
Q

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

A

Point D

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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  1
1   3
2  -1
-1  3
-2 -1
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5
Q

The function f(x)= 4x^3 + 6x^2 + 3x − 2 has a critical point at x = −1/2.Which sign chart describes this critical point?

A

-

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6
Q

What are the critical points of the function

f (x) = −2x^ 3 + 3x^ 2 + 36x − 68?

A

x = −2, 3

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7
Q

What is the minimum value that f (x) = 5x^ 2 + 10x − 4 attains?

A

-9

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8
Q

What is the x value at the maximum of f (x) = (1 − x)^1/3?

A

This function has no maximum

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9
Q

How many points of inflection are there for the graph of f(x) = x + 4/x?

A

0

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10
Q

On which of the following intervals is the graph of

f(x) = 6/x^2 + 3 concave up?

A

(−∞,−1) and (1,∞)

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11
Q

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

A

x=0 and x=2

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12
Q

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

A

(q,s)

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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)

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14
Q

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

A

(p, q)

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15
Q

The graph of f (x), which contains the point (1, 0), is shown. Which of the following statements about f (x) is true?

A

f ″(1) < f (1) < f ′(1)

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16
Q

On which interval is f (x) = x^ 3 − 3x ^2 − 9x + 1 increasing?

A

(−∞,−1) and (3,∞)

17
Q

Which of the following equations could be an equation of a vertical asymptote of y=x^2−2x / x^2−6x+8?

18
Q

Which of the following equations could be an equation of a vertical asymptote of y = x^2−9/x^2+9?

A

There is no vertical asymptote

19
Q

Which equation is represented by the following graph?

A

y = 2x^2+1 / x^2−x

20
Q

Which of the following represents the graph of

y = 1−x^2 / x^2−1?