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

$$f''(x) \u003c 0$$

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

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