$(-\infty, 0) \cup (2, \infty)$

$f(x)$ is not defined at $x = 4$

Question 1

Given the function $f(x) = x^4 - 4x^3$, what is the domain of $f(x)$?

Accepted Answer

$(-\infty, \infty)$

Question 2

For the function $f(x) = x^4 - 4x^3$, which of the following is a critical point?

Accepted Answer

$x = 0$

Question 3

Suppose $f(x) = \frac{x}{x^2 + 1}$. What is the horizontal asymptote of $f(x)$?

Accepted Answer

$y = 0$

Question 4

Which of the following statements about $f(x) = \frac{x}{x^2 + 1}$ is true?

Accepted Answer

$f(x)$ is an odd function

Question 5

For $f(x) = x^4 - 4x^3$, at which $x$-value does the function attain a local minimum?

Accepted Answer

$x = 3$

Question 6

Given $f(x) = x^4 - 4x^3$, what is the value of $f(3)$?

Accepted Answer

$-27$

Question 7

For $f(x) = x^4 - 4x^3$, which intervals is $f(x)$ decreasing?

Accepted Answer

$(-\infty, 0) \cup (0, 3)$

Question 8

For $f(x) = x^4 - 4x^3$, which of the following points is an inflection point?

Accepted Answer

$(0, 0)$

Question 9

Suppose $f(x) = \frac{x}{x^2 + 1}$. On which interval is $f(x)$ increasing?

Accepted Answer

$(-1, 1)$

Question 10

For $f(x) = x^4 - 4x^3$, what is the sign of $f''(x)$ on the interval $(0, 2)$?

Accepted Answer

$f''(x) < 0$

Question 11

Which of the following best describes the symmetry of $f(x) = x^4 - 4x^3$?

Accepted Answer

Neither even nor odd

Question 12

For $f(x) = x^4 - 4x^3$, what is the behavior of $f(x)$ as $x 	o \infty$?

Accepted Answer

$f(x) 	o \infty$

Question 13

Given $f(x) = \frac{x}{x^2 + 1}$, what is $f'(x)$?

Accepted Answer

$\frac{1 - x^2}{(x^2 + 1)^2}$

Question 14

For $f(x) = x^4 - 4x^3$, which of the following intervals is $f(x)$ concave up?

Accepted Answer

$(-\infty, 0) \cup (2, \infty)$

Question 15

Suppose $f(x)$ is continuous everywhere except at $x = 4$. Which of the following is true?

Accepted Answer

$f(x)$ is not defined at $x = 4$

Question 16

For $f(x) = x^4 - 4x^3$, what is the $x$-coordinate of the local maximum?

Accepted Answer

$x = 0$

Question 17

Given $f(x) = x^4 - 4x^3$, what is $f''(x)$?

Accepted Answer

$12x^2 - 24x$

Question 18

For $f(x) = x^4 - 4x^3$, at which $x$-values does $f''(x) = 0$?

Accepted Answer

$x = 0$ and $x = 2$

Question 19

Suppose $f(x) = \frac{x}{x^2 + 1}$. What is the value of $f(1)$?

Accepted Answer

$\frac{1}{2}$

(L16) Graphing Functions in Business Calculus: Guidelines, Analysis, and Examples

Study Guide - Practice Questions