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Calculus for Business, Economics, Life Sciences, and Social Sciences 13th

Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Chapter 4

Graphing and Optimization

Educators


Problem 1

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.
$g(x)=|x|$ on $(-\infty, 0)$

Dwijendra R.
Numerade Educator

Problem 2

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.
$m(x)=x^{3}$ on $(0, \infty)$

Dwijendra R.
Numerade Educator

Problem 3

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.
$f(x)=x$ on $(-\infty, \infty)$

Dwijendra R.
Numerade Educator

Problem 4

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.
$k(x)=-x^{2}$ on $(0, \infty)$

Dwijendra R.
Numerade Educator

Problem 5

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.
$p(x)=\sqrt[3]{x}$ on $(-\infty, 0)$

Dwijendra R.
Numerade Educator

Problem 6

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.
$h(x)=x^{2}$ on $(-\infty, 0)$

Dwijendra R.
Numerade Educator

Problem 7

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.
$r(x)=4-\sqrt{x}$ on $(0, \infty)$

Dwijendra R.
Numerade Educator

Problem 8

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.
$g(x)=|x|$ on $(0, \infty)$

Dwijendra R.
Numerade Educator

Problem 9

Refer to the following graph of $y=f(x)$
Identify the intervals on which $f(x)$ is increasing.

Dwijendra R.
Numerade Educator

Problem 10

Refer to the following graph of $y=f(x)$
Identify the intervals on which $f(x)$ is decreasing.

Dwijendra R.
Numerade Educator

Problem 11

Refer to the following graph of $y=f(x)$
Identify the intervals on which $f^{\prime}(x)<0$

Dwijendra R.
Numerade Educator

Problem 12

Refer to the following graph of $y=f(x)$
Identify the intervals on which $f^{\prime}(x)>0 .$

Dwijendra R.
Numerade Educator

Problem 13

Refer to the following graph of $y=f(x)$
Identify the $x$ coordinates of the points where $f^{\prime}(x)=0$.

Dwijendra R.
Numerade Educator

Problem 14

Refer to the following graph of $y=f(x)$
Identify the $x$ coordinates of the points where $f^{\prime}(x)$ does not exist.

Dwijendra R.
Numerade Educator

Problem 15

Refer to the following graph of $y=f(x)$
Identify the $x$ coordinates of the points where $f(x)$ has a local maximum.

Dwijendra R.
Numerade Educator

Problem 16

Refer to the following graph of $y=f(x)$
Identify the $x$ coordinates of the points where $f(x)$ has a local minimum.

Dwijendra R.
Numerade Educator

Problem 17

$f(x)$ is continuous on $(-\infty, \infty)$ and has critical numbers at $x=a, b, c,$ and $d$. Use the sign chart for $f^{\prime}(x)$ to determine whether $f$ has a local maximum, a local minimum, or neither at each critical number.

Dwijendra R.
Numerade Educator

Problem 18

$f(x)$ is continuous on $(-\infty, \infty)$ and has critical numbers at $x=a, b, c,$ and $d$. Use the sign chart for $f^{\prime}(x)$ to determine whether $f$ has a local maximum, a local minimum, or neither at each critical number.

Dwijendra R.
Numerade Educator

Problem 19

Give the local extrema off and match the graph off with one of the sign charts $a$ - $h$ in the figure on page $250 .$

Dwijendra R.
Numerade Educator

Problem 20

Give the local extrema off and match the graph off with one of the sign charts $a$ - $h$ in the figure on page $250 .$

Dwijendra R.
Numerade Educator

Problem 21

Give the local extrema off and match the graph off with one of the sign charts $a$ - $h$ in the figure on page $250 .$

Dwijendra R.
Numerade Educator

Problem 22

Give the local extrema off and match the graph off with one of the sign charts $a$ - $h$ in the figure on page $250 .$

Dwijendra R.
Numerade Educator

Problem 23

Give the local extrema off and match the graph off with one of the sign charts $a$ - $h$ in the figure on page $250 .$

Dwijendra R.
Numerade Educator

Problem 24

Give the local extrema off and match the graph off with one of the sign charts $a$ - $h$ in the figure on page $250 .$

Dwijendra R.
Numerade Educator

Problem 25

Give the local extrema off and match the graph off with one of the sign charts $a$ - $h$ in the figure on page $250 .$

Dwijendra R.
Numerade Educator

Problem 26

Give the local extrema off and match the graph off with one of the sign charts $a$ - $h$ in the figure on page $250 .$

Dwijendra R.
Numerade Educator

Problem 27

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.
$f(x)=x^{3}-12 x+8$

Dwijendra R.
Numerade Educator

Problem 28

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.
$f(x)=x^{3}-27 x+30$

Dwijendra R.
Numerade Educator

Problem 29

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.
$f(x)=\frac{6}{x+2}$

Dwijendra R.
Numerade Educator

Problem 30

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.
$f(x)=\frac{5}{x-4}$

Dwijendra R.
Numerade Educator

Problem 31

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.
$f(x)=|x|$

Dwijendra R.
Numerade Educator

Problem 32

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.
$f(x)=|x+3|$

Dwijendra R.
Numerade Educator

Problem 33

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=2 x^{2}-4 x$

Dwijendra R.
Numerade Educator

Problem 34

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=-3 x^{2}-12 x$

Dwijendra R.
Numerade Educator

Problem 35

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=-2 x^{2}-16 x-25$

Dwijendra R.
Numerade Educator

Problem 36

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=-3 x^{2}+12 x-5$

Dwijendra R.
Numerade Educator

Problem 37

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=x^{3}+4 x-5$

Dwijendra R.
Numerade Educator

Problem 38

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=-x^{3}-4 x+8$

Dwijendra R.
Numerade Educator

Problem 39

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=2 x^{3}-3 x^{2}-36 x$

Dwijendra R.
Numerade Educator

Problem 40

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=-2 x^{3}+3 x^{2}+120 x$

Dwijendra R.
Numerade Educator

Problem 41

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=3 x^{4}-4 x^{3}+5$

Dwijendra R.
Numerade Educator

Problem 42

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=x^{4}+2 x^{3}+5$

Dwijendra R.
Numerade Educator

Problem 43

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=(x-1) e^{-x}$

Dwijendra R.
Numerade Educator

Problem 44

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=x \ln x-x$

Dwijendra R.
Numerade Educator

Problem 45

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=4 x^{1 / 3}-x^{2 / 3}$

Dwijendra R.
Numerade Educator

Problem 46

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=\left(x^{2}-9\right)^{2 / 3}$

Dwijendra R.
Numerade Educator

Problem 47

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=x^{4}-4 x^{3}+9 x$

Dwijendra R.
Numerade Educator

Problem 48

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=x^{4}+5 x^{3}-15 x$

Dwijendra R.
Numerade Educator

Problem 49

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=x \ln x-(x-2)$

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Problem 50

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=e^{-x}-3 x^{2}$

Dwijendra R.
Numerade Educator

Problem 51

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=e^{x}-2 x^{2}$

Dwijendra R.
Numerade Educator

Problem 52

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.
$f(x)=\frac{\ln x}{x}-5 x+x^{2}$

Dwijendra R.
Numerade Educator

Problem 53

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.
$f(x)=4+8 x-x^{2}$

Dwijendra R.
Numerade Educator

Problem 54

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.
$f(x)=2 x^{2}-8 x+9$

Dwijendra R.
Numerade Educator

Problem 55

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.
$f(x)=x^{3}-3 x+1$

Dwijendra R.
Numerade Educator

Problem 56

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.
$f(x)=x^{3}-12 x+2$

Dwijendra R.
Numerade Educator

Problem 57

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.
$f(x)=10-12 x+6 x^{2}-x^{3}$

Dwijendra R.
Numerade Educator

Problem 58

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.
$f(x)=x^{3}+3 x^{2}+3 x$

Dwijendra R.
Numerade Educator

Problem 59

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.
$f(x)=x^{4}-18 x^{2}$

Dwijendra R.
Numerade Educator

Problem 60

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.
$f(x)=-x^{4}+50 x^{2}$

Dwijendra R.
Numerade Educator

Problem 61

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

Aman G.
Numerade Educator

Problem 62

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

Aman G.
Numerade Educator

Problem 63

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

Aman G.
Numerade Educator

Problem 64

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

Aman G.
Numerade Educator

Problem 65

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.
$f(-2)=4, f(0)=0, f(2)=-4$
$f^{\prime}(-2)=0, f^{\prime}(0)=0, f^{\prime}(2)=0$
$f^{\prime}(x)>0$ on $(-\infty,-2)$ and $(2, \infty)$
$f^{\prime}(x)<0$ on (-2,0) and (0,2)

Aman G.
Numerade Educator

Problem 66

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.
$f(-2)=-1, f(0)=0, f(2)=1$
$f^{\prime}(-2)=0, f^{\prime}(2)=0$
$f^{\prime}(x)>0$ on $(-\infty,-2),(-2,2),$ and $(2, \infty)$

Aman G.
Numerade Educator

Problem 67

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.
$f(-1)=2, f(0)=0, f(1)=-2 ;$
$f^{\prime}(-1)=0, f^{\prime}(1)=0, f^{\prime}(0)$ is not defined;
$f^{\prime}(x)>0$ on $(-\infty,-1)$ and $(1, \infty)$
$f^{\prime}(x)<0$ on (-1,0) and (0,1)

Aman G.
Numerade Educator

Problem 68

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.
$f(-1)=2, f(0)=0, f(1)=2$
$f^{\prime}(-1)=0, f^{\prime}(1)=0, f^{\prime}(0)$ is not defined;
$f^{\prime}(x)>0$ on $(-\infty,-1)$ and (0,1)
$f^{\prime}(x)<0$ on (-1,0) and $(1, \infty)$

Aman G.
Numerade Educator

Problem 69

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.
$f_{1}$

Aman G.
Numerade Educator

Problem 70

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.
$f_{2}$

Aman G.
Numerade Educator

Problem 71

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.
$f_{3}$

Aman G.
Numerade Educator

Problem 72

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.
$f_{4}$

Aman G.
Numerade Educator

Problem 73

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.
$f_{5}$

Aman G.
Numerade Educator

Problem 74

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.
$f_{6}$

Aman G.
Numerade Educator

Problem 75

Use the given graph of $y=f^{\prime}(x)$ to find the intervals on which $f$ is increasing, the intervals on which $f$ is decreasing, and the x coordinates of the local extrema off. Sketch a possible graph of $y=f(x)$.

Aman G.
Numerade Educator

Problem 76

Use the given graph of $y=f^{\prime}(x)$ to find the intervals on which $f$ is increasing, the intervals on which $f$ is decreasing, and the x coordinates of the local extrema off. Sketch a possible graph of $y=f(x)$.

Aman G.
Numerade Educator

Problem 77

Use the given graph of $y=f^{\prime}(x)$ to find the intervals on which $f$ is increasing, the intervals on which $f$ is decreasing, and the x coordinates of the local extrema off. Sketch a possible graph of $y=f(x)$.

Aman G.
Numerade Educator

Problem 78

Use the given graph of $y=f^{\prime}(x)$ to find the intervals on which $f$ is increasing, the intervals on which $f$ is decreasing, and the x coordinates of the local extrema off. Sketch a possible graph of $y=f(x)$.

Aman G.
Numerade Educator

Problem 79

Use the given graph of $y=f^{\prime}(x)$ to find the intervals on which $f$ is increasing, the intervals on which $f$ is decreasing, and the x coordinates of the local extrema off. Sketch a possible graph of $y=f(x)$.

Aman G.
Numerade Educator

Problem 80

Use the given graph of $y=f^{\prime}(x)$ to find the intervals on which $f$ is increasing, the intervals on which $f$ is decreasing, and the x coordinates of the local extrema off. Sketch a possible graph of $y=f(x)$.

Aman G.
Numerade Educator

Problem 81

Use the given graph of $y=f(x)$ to find the intervals on which $f^{\prime}(x)>0,$ the intervals on which $f^{\prime}(x)<0,$ and the values of $x$ for which $f^{\prime}(x)=0 .$ Sketch a possible graph of $y=f^{\prime}(x)$.

Aman G.
Numerade Educator

Problem 82

Use the given graph of $y=f(x)$ to find the intervals on which $f^{\prime}(x)>0,$ the intervals on which $f^{\prime}(x)<0,$ and the values of $x$ for which $f^{\prime}(x)=0 .$ Sketch a possible graph of $y=f^{\prime}(x)$.

Aman G.
Numerade Educator

Problem 83

Use the given graph of $y=f(x)$ to find the intervals on which $f^{\prime}(x)>0,$ the intervals on which $f^{\prime}(x)<0,$ and the values of $x$ for which $f^{\prime}(x)=0 .$ Sketch a possible graph of $y=f^{\prime}(x)$.

Aman G.
Numerade Educator

Problem 84

Use the given graph of $y=f(x)$ to find the intervals on which $f^{\prime}(x)>0,$ the intervals on which $f^{\prime}(x)<0,$ and the values of $x$ for which $f^{\prime}(x)=0 .$ Sketch a possible graph of $y=f^{\prime}(x)$.

Aman G.
Numerade Educator

Problem 85

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.
$f(x)=x+\frac{4}{x}$

Aman G.
Numerade Educator

Problem 86

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.
$f(x)=\frac{9}{x}+x$

Aman G.
Numerade Educator

Problem 87

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.
$f(x)=1+\frac{1}{x}+\frac{1}{x^{2}}$

Aman G.
Numerade Educator

Problem 88

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.
$f(x)=3-\frac{4}{x}-\frac{2}{x^{2}}$

Aman G.
Numerade Educator

Problem 89

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.
$f(x)=\frac{x^{2}}{x-2}$

Aman G.
Numerade Educator

Problem 90

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.
$f(x)=\frac{x^{2}}{x+1}$

Aman G.
Numerade Educator

Problem 91

The graph of the total profit $P(x)$ (in dollars) from the sale of $x$ cordless electric screwdrivers is shown in the figure.
(A) Write a brief description of the graph of the marginal profit function $y=P^{\prime}(x)$, including a discussion of any $x$ intercepts.
(B) Sketch a possible graph of $y=P^{\prime}(x)$.

Aman G.
Numerade Educator

Problem 92

The graph of the total revenue $R(x)$ (in dollars) from the sale of $x$ cordless electric screwdrivers is shown in the figure.
(A) Write a brief description of the graph of the marginal revenue function $y=R^{\prime}(x),$ including a discussion of any $x$ intercepts.
(B) Sketch a possible graph of $y=R^{\prime}(x)$.

Aman G.
Numerade Educator

Problem 93

The figure approximates the rate of change of the price of bacon over a 70 -month period, where $B(t)$ is the price of a pound of sliced bacon (in dollars) and $t$ is time (in months).
(A) Write a brief description of the graph of $y=B(t)$, including a discussion of any local extrema.
(B) Sketch a possible graph of $y=B(t)$.

Aman G.
Numerade Educator

Problem 94

The figure approximates the rate of change of the price of eggs over a 70 -month period, where $E(t)$ is the price of a dozen eggs (in dollars) and $t$ is time (in months).
(A) Write a brief description of the graph of $y=E(t)$, including a discussion of any local extrema.
(B) Sketch a possible graph of $y=E(t)$.

Aman G.
Numerade Educator

Problem 95

A manufacturer incurs the following costs in producing $x$ water ski vests in one day, for $0<x<150$ : fixed costs, $\$ 320 ;$ unit production cost, $\$ 20$ per vest; equipment maintenance and repairs, $0.05 x^{2}$ dollars. So, the cost of manufacturing $x$ vests in one day is given by
$$
C(x)=0.05 x^{2}+20 x+320 \quad 0<x<150
$$
(A) What is the average $\operatorname{cost} \bar{C}(x)$ per vest if $x$ vests are produced in one day?
(B) Find the critical numbers of $\bar{C}(x),$ the intervals on which the average cost per vest is decreasing, the intervals on which the average cost per vest is increasing, and the local extrema. Do not graph.

Aman G.
Numerade Educator

Problem 96

A manufacturer incurs the following costs in producing $x$ rain jackets in one day for $0<x<200$ : fixed costs, $\$ 450 ;$ unit production cost, $\$ 30$ per jacket; equipment maintenance and repairs, $0.08 x^{2}$ dollars.
(A) What is the average cost $\bar{C}(x)$ per jacket if $x$ jackets are produced in one day?
(B) Find the critical numbers of $\bar{C}(x),$ the intervals on which the average cost per jacket is decreasing, the intervals on which the average cost per jacket is increasing, and the local extrema. Do not graph.

Aman G.
Numerade Educator

Problem 97

A drug is injected into the bloodstream of a patient through the right arm. The drug concentration in the bloodstream of the left arm $t$ hours after the injection is approximated by
$$
C(t)=\frac{0.28 t}{t^{2}+4} \quad 0<t<24
$$
Find the critical numbers of $C(t),$ the intervals on which the drug concentration is increasing, the intervals on which the concentration of the drug is decreasing, and the local extrema. Do not graph.

Aman G.
Numerade Educator

Problem 98

The concentration $C(t),$ in milligrams per cubic centimeter, of a particular drug in a patient's bloodstream is given by
$$
C(t)=\frac{0.3 t}{t^{2}+6 t+9} \quad 0<t<12
$$
where $t$ is the number of hours after the drug is taken orally. Find the critical numbers of $C(t),$ the intervals on which the drug concentration is increasing, the intervals on which the drug concentration is decreasing, and the local extrema. Do not graph.

Aman G.
Numerade Educator