$$\begin{pmatrix} 6 & 8 \\ 10 & 12 \end{pmatrix}$$

$$\{x \mid x \neq -2, x \neq 2\}$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{16 - x^2$}$$?

Accepted Answer

$$[-4, 4]$$

Question 2

Given the function $$f(x) = e$$^{-x^2}$$, on which interval is the function concave up?

Accepted Answer

$$(-\infty, 0)$$

Question 3

If $$f(x) = x^3$ + x^2$, on which interval is f(x$$)$$ increasing?

Accepted Answer

$$(-\frac{2}{3}, \infty)$$

Question 4

A population of bacteria is modeled by $$P(t) = 300 - t\sqrt{100 - 2t}$$ for $$0 \leq t \leq 40. $$What is the critical point of $$P(t)$$?

Accepted Answer

$$t = 33.33 ($$where $$3t - 100 = 0)$$

Question 5

Which of the following is the correct formula for the tangent line to $$f(x) at$$ $$x = a$$?

Accepted Answer

$$y = f(a) + f'(a)(x - a)$$

Question 6

Suppose the cost function for producing $$q$$ items is $$C(q) = q^3$ - 9q^2$ + 27q + 8. $$What are the fixed costs?

Accepted Answer

$$8$$

Question 7

If $$f(x) = \ln(x^2$ + 9)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 8

Given the function $$f(x) = |x - 1| \u003e 2$$, which of the following is the solution set?

Accepted Answer

$$x  3$$

Question 9

A department store issues a credit card with an interest rate of 2% per month. What is the effective annual rate (EAR)?

Accepted Answer

$$(1.02)^{12} - 1$

Question 10

Which of the following best describes the amplitude and period of the function $$y = 3\sin(2t) + 1$$?

Accepted Answer

Amplitude: $$3$$, Period: $$\pi$$

Question 11

If $$f(x) = x^2$ - 4$$, what is the domain of $$f(x) in $$set notation?

Accepted Answer

$$\{x \mid x \in \mathbb{R}\}$$

Question 12

Given the matrix $$A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 5 & 6 \ 7 & 8 \end{pmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{pmatrix} 6 & 8 \ 10 & 12 \end{pmatrix}$$

Question 13

Which of the following is the correct application of the chain rule to $$f(x) = \sin(3x^2$)$$?

Accepted Answer

$$f'(x) = \cos(3x^2$) \cdot 6x$$

Question 14

If $$f(x) = \ln(x)$$, what is the derivative $$f'(x)$$?

Accepted Answer

$$\frac{1}{x}$$

Question 15

Which of the following best describes the solution to the equation $$5 + e$$^{-0.1x}$$ = 10$$?

Accepted Answer

$$x = -10\ln(5)$$

Question 16

Given the function $$f(x) = x^2$ + x - 6$$, for which values of $$x is$$ $$f(x) \u003e 0$$?

Accepted Answer

$$x  2$$

Question 17

If $$f(x) = \frac{1}{x^2$ - 4}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$\{x \mid x 
eq -2, x 
eq 2\}$$

Question 18

Which of the following best describes the global maximum of a continuous function $$f(x) on a $$closed interval $$[a, b]$$?

Accepted Answer

The largest value of $$f(x)$$ for $$x in$$ $$[a, b]$$

WTW 134 Calculus Study Guide – University of Pretoria

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