Question 1

Find the largest open interval where the function is changing as requested.
-Increasing $y=\left(x^{2}-9\right)^{2}$

Accepted Answer

A)  $(3, \infty)$ 
B)  $(-3,0)$ 
C)  $(-3,3)$ 
D)  $(-\infty, 0)$ 
A)  $(3, \infty)$ 
B)  $(-3,0)$ 
C)  $(-3,3)$ 
D)  $(-\infty, 0)$ A

Question 2

Solve the problem.
-The correlation between respiratory rate and body mass in the first three years of life can be expressed by the function
$$\log R(w)=1.85-0.33 \log (w)$$
Where $\mathrm{w}$ is the body weight (in $\mathrm{kg}$ ) and $\mathrm{R}(\mathrm{w}$ ) is the respiratory rate (in breaths per minute). Find $R^{\prime}(w)$ using implicit differentiation.

Accepted Answer

A)  $R^{\prime}(w)=-23.36 w^{-0.67}$ 
B)  $R^{\prime}(w)=70.79 w^{-1.33}$ 
C)  $R^{\prime}(w)=-23.36 w^{-0.33}$ 
D)  $R^{\prime}(w)=-23.36 w^{-1.33}$ 
A)  $R^{\prime}(w)=-23.36 w^{-0.67}$ 
B)  $R^{\prime}(w)=70.79 w^{-1.33}$ 
C)  $R^{\prime}(w)=-23.36 w^{-0.33}$ 
D)  $R^{\prime}(w)=-23.36 w^{-1.33}$ D

Question 3

$\mathrm{s}$ is the distance (in $\mathrm{ft}$ ) traveled in time $\mathrm{t}$ (in s) by a particle. Find the velocity and acceleration at the given time.
-$s=\sqrt{t^{2}-5}, t=3$

Accepted Answer

A)  $\mathrm{v}=-\frac{5}{8} \mathrm{ft} / \mathrm{s}, \mathrm{a}=1.5 \mathrm{ft} / \mathrm{s}^{2}$ 
B)  $\mathrm{v}=1.5 \mathrm{ft} / \mathrm{s}, \mathrm{a}=-\frac{5}{8} \mathrm{ft} / \mathrm{s}^{2}$ 
C)  $\mathrm{v}=-1.5 \mathrm{ft} / \mathrm{s}, \mathrm{a}=\frac{5}{8} \mathrm{ft} / \mathrm{s}^{2}$ 
D)  $\mathrm{v}=\frac{5}{8} \mathrm{ft} / \mathrm{s}, \mathrm{a}=-1.5 \mathrm{ft} / \mathrm{s}^{2}$ 
A)  $\mathrm{v}=-\frac{5}{8} \mathrm{ft} / \mathrm{s}, \mathrm{a}=1.5 \mathrm{ft} / \mathrm{s}^{2}$ 
B)  $\mathrm{v}=1.5 \mathrm{ft} / \mathrm{s}, \mathrm{a}=-\frac{5}{8} \mathrm{ft} / \mathrm{s}^{2}$ 
C)  $\mathrm{v}=-1.5 \mathrm{ft} / \mathrm{s}, \mathrm{a}=\frac{5}{8} \mathrm{ft} / \mathrm{s}^{2}$ 
D)  $\mathrm{v}=\frac{5}{8} \mathrm{ft} / \mathrm{s}, \mathrm{a}=-1.5 \mathrm{ft} / \mathrm{s}^{2}$ B

Question 4

Find dy/dx by implicit differentiation.
-$x^{4 / 3}+y^{4 / 3}=1$

Accepted Answer

A)  $\left(\frac{x}{y}\right)^{1 / 3}$ 
B)  $-\left(\frac{y}{x}\right)^{1 / 3}$ 
C)  $\left(\frac{y}{x}\right)^{1 / 3}$ 
D)  $-\left(\frac{x}{y}\right)^{1 / 3}$ 
A)  $\left(\frac{x}{y}\right)^{1 / 3}$ 
B)  $-\left(\frac{y}{x}\right)^{1 / 3}$ 
C)  $\left(\frac{y}{x}\right)^{1 / 3}$ 
D)  $-\left(\frac{x}{y}\right)^{1 / 3}$

Question 5

Find dy/dx by implicit differentiation.
-$x y^{2}=4$

Accepted Answer

A)  $\frac{2 x}{y}$ 
B)  $-\frac{y}{2 x}$ 
C)  $-\frac{2 y}{x}$ 
D)  $\frac{x}{2 y}$ 
A)  $\frac{2 x}{y}$ 
B)  $-\frac{y}{2 x}$ 
C)  $-\frac{2 y}{x}$ 
D)  $\frac{x}{2 y}$

Question 6

Solve the problem.
-The price $P$ of a certain computer system decreases immediately after its introduction and then increases. If the price $P$ is estimated by the formula $P=150 t^{2}-2000 t+6600$, where $t$ is the time in months from its introduction, find the time until the minimum price is reached. Round to the nearest tenth if necessary.

Accepted Answer

A)  6.7 months 
B)  26.7 months 
C)  13.3 months 
D)  10 months 
A)  6.7 months 
B)  26.7 months 
C)  13.3 months 
D)  10 months

Question 7

Determine the location of each local extremum of the function.
-$f(x)=x^{3}-9 x^{2}+27 x+1$

Accepted Answer

A)  Local minimum at 3 
B)  Local maximum at 3 
C)  Local maximum at 3 ; local minimum at -3 
D)  No local extrema 
A)  Local minimum at 3 
B)  Local maximum at 3 
C)  Local maximum at 3 ; local minimum at -3 
D)  No local extrema

Question 8

Solve each problem.
-A piece of molding $182 \mathrm{~cm}$ long is to be cut to form a rectangular picture frame. What dimensions will enclose the largest area?

Accepted Answer

A)  $13.49 \mathrm{~cm} \times 45.5 \mathrm{~cm}$ 
B)  $36.4 \mathrm{~cm} \times 36.4 \mathrm{~cm}$ 
C)  $45.5 \mathrm{~cm} \times 45.5 \mathrm{~cm}$ 
D)  $13.49 \mathrm{~cm} \times 13.49 \mathrm{~cm}$ 
A)  $13.49 \mathrm{~cm} \times 45.5 \mathrm{~cm}$ 
B)  $36.4 \mathrm{~cm} \times 36.4 \mathrm{~cm}$ 
C)  $45.5 \mathrm{~cm} \times 45.5 \mathrm{~cm}$ 
D)  $13.49 \mathrm{~cm} \times 13.49 \mathrm{~cm}$

Question 9

Identify the intervals where the function is changing as requested.
-Increasing

Accepted Answer

A)  $(3, \infty)$ 
B)  $(-2, \infty)$ 
C)  $(-2,0)$ 
D)  $(3,6)$ 
A)  $(3, \infty)$ 
B)  $(-2, \infty)$ 
C)  $(-2,0)$ 
D)  $(3,6)$

Question 10

Solve the problem.
-A man $6 \mathrm{ft}$ tall walks at a rate of $6 \mathrm{ft} / \mathrm{s}$ away from a lamppost that is $12 \mathrm{ft}$ high. At what rate is the length of his shadow changing when he is $45 \mathrm{ft}$ away from the lamppost?

Accepted Answer

A)  $1 \mathrm{ft} / \mathrm{s}$ 
B)  $2 \mathrm{ft} / \mathrm{s}$ 
C)  $45 \mathrm{ft} / \mathrm{s}$ 
D)  $6 \mathrm{ft} / \mathrm{s}$ 
A)  $1 \mathrm{ft} / \mathrm{s}$ 
B)  $2 \mathrm{ft} / \mathrm{s}$ 
C)  $45 \mathrm{ft} / \mathrm{s}$ 
D)  $6 \mathrm{ft} / \mathrm{s}$

Question 11

Determine the location of each local extremum of the function.
-$f(x)=-x^{3}-1.5 x^{2}+36 x+3$

Accepted Answer

A)  Local maximum at 4 ; local minimum at -3 
B)  Local maximum at -4 ; local minimum at 3 
C)  Local maximum at 3 ; local minimum at -4 
D)  Local maximum at -3 ; local minimum at 4 
A)  Local maximum at 4 ; local minimum at -3 
B)  Local maximum at -4 ; local minimum at 3 
C)  Local maximum at 3 ; local minimum at -4 
D)  Local maximum at -3 ; local minimum at 4

Question 12

The rule of the derivative of a function $f$ is given. Find the location of all points of inflection of the function $f$.
-$f^{\prime}(x)=\left(x^{2}-4\right)(x+3)$

Accepted Answer

A)  -1 
B)  $2,-3$ 
C)  $-2,-3,2$ 
D)  $-2.53,0.53$ 
A)  -1 
B)  $2,-3$ 
C)  $-2,-3,2$ 
D)  $-2.53,0.53$

Question 13

Find the location and value of each local extremum for the function.
-

Accepted Answer

A)  $(2,0)$ 
B)  None 
C)  $(-2,3)$ 
D)  $(-2,3),(2,0)$ 
A)  $(2,0)$ 
B)  None 
C)  $(-2,3)$ 
D)  $(-2,3),(2,0)$

Question 14

Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema.
-$f(x)=x^{4}-4 x^{3}-53 x^{2}-86 x+5$

Accepted Answer

A)  Approximate local maximum at -0.944 ; approximate local minima at -3.192 and 7.136 
B)  Approximate local maximum at 1.02 ; approximate local minima at -3.167 and 7.046 
C)  Approximate local maximum at 0.852 ; approximate local minima at -3.234 and 7.127 
D)  Approximate local maximum at 0.935 ; approximate local minima at -3.119 and 7.198 
A)  Approximate local maximum at -0.944 ; approximate local minima at -3.192 and 7.136 
B)  Approximate local maximum at 1.02 ; approximate local minima at -3.167 and 7.046 
C)  Approximate local maximum at 0.852 ; approximate local minima at -3.234 and 7.127 
D)  Approximate local maximum at 0.935 ; approximate local minima at -3.119 and 7.198

Question 15

Solve the problem.
-A product sells by word of mouth. The company that produces the product has noticed that revenue from sales is given by $R(t)=2 \sqrt{x}$, where $x$ is the number of units produced and sold. If the revenue keeps changing at a rate of $\$ 700$ per month, how fast is the rate of sales changing when 300 units have been made and sold? (Round to the nearest dollar per month.)

Accepted Answer

A)  $\$ 48,497 /$ month 
B)  $\$ 40 /$ month 
C)  $\$ 12,124 /$ month 
D)  $\$ 6062 /$ month 
A)  $\$ 48,497 /$ month 
B)  $\$ 40 /$ month 
C)  $\$ 12,124 /$ month 
D)  $\$ 6062 /$ month

Question 16

Find the absolute extremum within the specified domain.
-Maximum of $f(x)=\frac{x+3}{x-3} ;[-4,4]$

Accepted Answer

A)  $(4,7)$ 
B)  $(0,-1)$ 
C)  $(-4,7)$ 
D)  None 
A)  $(4,7)$ 
B)  $(0,-1)$ 
C)  $(-4,7)$ 
D)  None

Question 17

Find $\frac{d y}{d x}$ at the given point.
-$2 x y-2 x+y=-14 ;(2,-2)$

Accepted Answer

A)  $\frac{6}{5}$ 
B)  $-\frac{6}{5}$ 
C)  $-\frac{5}{6}$ 
D)  $\frac{5}{6}$ 
A)  $\frac{6}{5}$ 
B)  $-\frac{6}{5}$ 
C)  $-\frac{5}{6}$ 
D)  $\frac{5}{6}$

Question 18

A rectangular field is to be enclosed on four sides with a fence. Fencing costs $\$ 5$ per foot for two opposite sides, and $\$ 6$ per foot for the other two sides. Find the dimensions of the field of area $710 \mathrm{ft}^{2}$ that would be the cheapest to enclose. Round to the nearest tenth.

Accepted Answer

A)  $22.2 \mathrm{ft} @ \$ 5$ by $32 \mathrm{ft} @ \$ 6$ 
B)  $24.3 \mathrm{ft} @ \$ 5$ by $29.2 \mathrm{ft} @ \$ 6$ 
C)  $29.2 \mathrm{ft} @ \$ 5$ by $24.3 \mathrm{ft} @ \$ 6$ 
D)  $32 \mathrm{ft} @ \$ 5$ by $22.2 \mathrm{ft} @ \$ 6$ 
A)  $22.2 \mathrm{ft} @ \$ 5$ by $32 \mathrm{ft} @ \$ 6$ 
B)  $24.3 \mathrm{ft} @ \$ 5$ by $29.2 \mathrm{ft} @ \$ 6$ 
C)  $29.2 \mathrm{ft} @ \$ 5$ by $24.3 \mathrm{ft} @ \$ 6$ 
D)  $32 \mathrm{ft} @ \$ 5$ by $22.2 \mathrm{ft} @ \$ 6$

Question 19

Solve the problem.
-At a certain copy center, the cost $y$ (in dollars) of purchasing $x$ thousand printed cards can be approximated by $x y+y=60 x$. Use implicit differentiation to find and interpret $\frac{d y}{d x}$ when $x=1$ and $\mathrm{y}=30$.

Accepted Answer

A)  $\frac{d y}{d x}=15$ means that additional cards will cost approximately $\$ 15.00$ each. 
B)  $\frac{d y}{d x}=30$ means that ordering an additional thousand cards will cost approximately $\$ 15.00$ more. 
C)  $\frac{d y}{d x}=15$ means that ordering an additional thousand cards will cost approximately $\$ 15.00$ more. 
D)  $\frac{d y}{d x}=30$ means that ordering an additional 30 cards will cost $\$ 1000.00$ more. 
A)  $\frac{d y}{d x}=15$ means that additional cards will cost approximately $\$ 15.00$ each. 
B)  $\frac{d y}{d x}=30$ means that ordering an additional thousand cards will cost approximately $\$ 15.00$ more. 
C)  $\frac{d y}{d x}=15$ means that ordering an additional thousand cards will cost approximately $\$ 15.00$ more. 
D)  $\frac{d y}{d x}=30$ means that ordering an additional 30 cards will cost $\$ 1000.00$ more.

Question 20

Solve each problem.
-A rectangular field is to be enclosed on four sides with a fence. Fencing costs $\$ 8$ per foot for two opposite sides, and $\$ 4$ per foot for the other two sides. Find the dimensions of the field of area $800 \mathrm{ft}^{2}$ that would be the cheapest to enclose.

Accepted Answer

A)  $40 \mathrm{ft} @ \$ 8$ by $20 \mathrm{ft} @ \$ 4$ 
B)  $20 \mathrm{ft} @ \$ 8$ by $40 \mathrm{ft} @ \$ 4$ 
C)  $14.1 \mathrm{ft} @ \$ 8$ by $56.6 \mathrm{ft} @ \$ 4$ 
D)  $56.6 \mathrm{ft} @ \$ 8$ by $14.1 \mathrm{ft} @ \$ 4$ 
A)  $40 \mathrm{ft} @ \$ 8$ by $20 \mathrm{ft} @ \$ 4$ 
B)  $20 \mathrm{ft} @ \$ 8$ by $40 \mathrm{ft} @ \$ 4$ 
C)  $14.1 \mathrm{ft} @ \$ 8$ by $56.6 \mathrm{ft} @ \$ 4$ 
D)  $56.6 \mathrm{ft} @ \$ 8$ by $14.1 \mathrm{ft} @ \$ 4$

Find the largest open interval where the function is changing as requested. -Increasing $y=\left(x^{2}-9\right)^{2}$

$\mathrm{s}$ is the distance (in $\mathrm{ft}$ ) traveled in time $\mathrm{t}$ (in s) by a particle. Find the velocity and acceleration at the given time. - $s=\sqrt{t^{2}-5}, t=3$

Find dy/dx by implicit differentiation. - $x^{4 / 3}+y^{4 / 3}=1$

Find dy/dx by implicit differentiation. - $x y^{2}=4$

Determine the location of each local extremum of the function. - $f(x)=x^{3}-9 x^{2}+27 x+1$

Solve each problem. -A piece of molding $182 \mathrm{~cm}$ long is to be cut to form a rectangular picture frame. What dimensions will enclose the largest area?

Identify the intervals where the function is changing as requested. -Increasing

Solve the problem. -A man $6 \mathrm{ft}$ tall walks at a rate of $6 \mathrm{ft} / \mathrm{s}$ away from a lamppost that is $12 \mathrm{ft}$ high. At what rate is the length of his shadow changing when he is $45 \mathrm{ft}$ away from the lamppost?

Determine the location of each local extremum of the function. - $f(x)=-x^{3}-1.5 x^{2}+36 x+3$

The rule of the derivative of a function $f$ is given. Find the location of all points of inflection of the function $f$ . - $f^{\prime}(x)=\left(x^{2}-4\right)(x+3)$

Find the location and value of each local extremum for the function. -

Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema. - $f(x)=x^{4}-4 x^{3}-53 x^{2}-86 x+5$

Find the absolute extremum within the specified domain. -Maximum of $f(x)=\frac{x+3}{x-3} ;[-4,4]$

Find $\frac{d y}{d x}$ at the given point. - $2 x y-2 x+y=-14 ;(2,-2)$

A rectangular field is to be enclosed on four sides with a fence. Fencing costs $\$ 5$ per foot for two opposite sides, and $\$ 6$ per foot for the other two sides. Find the dimensions of the field of area $710 \mathrm{ft}^{2}$ that would be the cheapest to enclose. Round to the nearest tenth.

Solve the problem. -At a certain copy center, the cost $y$ (in dollars) of purchasing $x$ thousand printed cards can be approximated by $x y+y=60 x$ . Use implicit differentiation to find and interpret $\frac{d y}{d x}$ when $x=1$ and $\mathrm{y}=30$ .

Solve each problem. -A rectangular field is to be enclosed on four sides with a fence. Fencing costs $\$ 8$ per foot for two opposite sides, and $\$ 4$ per foot for the other two sides. Find the dimensions of the field of area $800 \mathrm{ft}^{2}$ that would be the cheapest to enclose.

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Exponential and Logarithmic Functions

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Systems of Linear Equations and Matrices

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Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

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Exam 12: Applications of the Derivative

Find the largest open interval where the function is changing as requested. -Increasing y=(x2−9)2y=\left(x^{2}-9\right)^{2}y=(x2−9)2

s\mathrm{s}s is the distance (in ft\mathrm{ft}ft ) traveled in time t\mathrm{t}t (in s) by a particle. Find the velocity and acceleration at the given time. - s=t2−5,t=3s=\sqrt{t^{2}-5}, t=3s=t2−5​,t=3

Find dy/dx by implicit differentiation. - x4/3+y4/3=1x^{4 / 3}+y^{4 / 3}=1x4/3+y4/3=1

Find dy/dx by implicit differentiation. - xy2=4x y^{2}=4xy2=4

Determine the location of each local extremum of the function. - f(x)=x3−9x2+27x+1f(x)=x^{3}-9 x^{2}+27 x+1f(x)=x3−9x2+27x+1

Solve each problem. -A piece of molding 182 cm182 \mathrm{~cm}182 cm long is to be cut to form a rectangular picture frame. What dimensions will enclose the largest area?