Question 1

Find the relative maximum and minimum points of the function $f(x)=x^{3}-x^{2}+15 x+8$.

Accepted Answer

A)  Relative maximum at $(1,15)$; relative minimum at $(5,-17)$. 
B)  Relative maximum at (7, 15); relative minimum at ( $-1,-17$ ). 
C)  Relative maximum at $(8,64)$; relative minimum at $(-2,-66)$. 
D)  Relative maximum at $(5,15)$; relative minimum at $(1,-17)$. 
A)  Relative maximum at $(1,15)$; relative minimum at $(5,-17)$. 
B)  Relative maximum at (7, 15); relative minimum at ( $-1,-17$ ). 
C)  Relative maximum at $(8,64)$; relative minimum at $(-2,-66)$. 
D)  Relative maximum at $(5,15)$; relative minimum at $(1,-17)$. A

Question 2

In the problems below, find any relative maximum or minimum values of each function.
-Given $f(x)=\frac{6}{x^{2}-9}$, find a) the intervals for which $f(x)$ is increasing and decreasing, b) relative maximums and relative minimums, $\mathrm{c}$ ) intervals for which $\mathrm{f}(\mathrm{x})$ is concave upward and concave downward, and d) points of inflection. Sketch the curve.

Accepted Answer

a) increasing for x < -3, -3< x < 0; decreasing for 0 < x < 3, x > 3 b) rel max at [0, $\frac{-2}{3}$] c) critical points ±3, 2± $\sqrt{13}$ , concave upward for x < -3, x > 3, concave downward for -3 < x <3 d) no point of inflection

Question 3

Use Newton's Method to find a solution to six significant digits in the given interval.
- $x^{4}-5 x^{2}-6=0 ; 2 \leq x \leq 4$

Accepted Answer

2.44949

Question 4

Name the horizontal and vertical asymptotes of the function $f(x)=\frac{3 x}{x^{2}-16}$.

Accepted Answer

A)  Horizontal: $\mathrm{y}=3$; vertical: $\mathrm{x}=4$ and $\mathrm{x}=-4$. 
B)  Horizontal: $\mathrm{y}=0$; vertical: $\mathrm{x}=4$ and $\mathrm{x}=-4$. 
C)  Horizontal: $\mathrm{y}=0$; vertical: $\mathrm{x}=4$. 
D)  Horizontal: $\mathrm{y}=3$; vertical: $\mathrm{x}=4$. 
A)  Horizontal: $\mathrm{y}=3$; vertical: $\mathrm{x}=4$ and $\mathrm{x}=-4$. 
B)  Horizontal: $\mathrm{y}=0$; vertical: $\mathrm{x}=4$ and $\mathrm{x}=-4$. 
C)  Horizontal: $\mathrm{y}=0$; vertical: $\mathrm{x}=4$. 
D)  Horizontal: $\mathrm{y}=3$; vertical: $\mathrm{x}=4$.

Question 5

A rectangular, $450 \mathrm{ft}^{2}$ family room addition is to be built using the existing house for one of its walls. Find a function $\mathrm{f}(\mathrm{x})$ that would represent the total length of the other 3 walls that need to be built, where $x$ represents the length of the wall that will be parallel to the existing wall.

Accepted Answer

A)  $f(x)=2 x+\frac{900}{x}$ 
B)  $f(x)=x+\frac{450}{x}$ 
C)  $f(x)=x+\frac{900}{x}$ 
D)  $f(x)=3 x-\frac{450}{x}$ 
A)  $f(x)=2 x+\frac{900}{x}$ 
B)  $f(x)=x+\frac{450}{x}$ 
C)  $f(x)=x+\frac{900}{x}$ 
D)  $f(x)=3 x-\frac{450}{x}$

Question 6

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the $\mathrm{x}$ - axis, symmetry, and asymptotes. Graph each equation.
-  $y=x^{3}-5 x^{2}-12 x+36$

Accepted Answer

None

Question 7

Use Newton's Method to find a solution to six significant digits in the given interval.
- $x^{3}-2 x^{2}=8 x-6 ; 3 \leq x \leq 5$

Accepted Answer

The answer of Use Newton's Method to find a solution...

Question 8

A rectangular box, open at the top, with a square base is to have a volume of $13,500 \mathrm{~cm}^{3}$. Find the dimensions if the box is to contain the least amount of material.

Accepted Answer

The answer of A rectangular box, open at the top,...

Question 9

The area of a square in terms of its diagonal $z$ is given by the formula $A=\frac{1}{2} z^{2}$. Use a differential to estimate the change in the area of a square whose diagonal has been increased from $6.0 \mathrm{~cm}$ to 6.2 $\mathrm{cm}$.

Accepted Answer

A)  $\mathrm{dA}=1.2 \mathrm{~cm}^{2}$ 
B)  $\mathrm{dA}=1.8 \mathrm{~cm}^{2}$ 
C)  $\mathrm{dA}=0.4 \mathrm{~cm}^{2}$ 
D)  $\mathrm{dA}=0.2 \mathrm{~cm}^{2}$ 
A)  $\mathrm{dA}=1.2 \mathrm{~cm}^{2}$ 
B)  $\mathrm{dA}=1.8 \mathrm{~cm}^{2}$ 
C)  $\mathrm{dA}=0.4 \mathrm{~cm}^{2}$ 
D)  $\mathrm{dA}=0.2 \mathrm{~cm}^{2}$

Question 10

A circular plate is being heated so that its radius is increasing at a rate of $0.09 \mathrm{in}$./h. How fast is its area increasing when its radius is 15 inches?

Accepted Answer

The answer of A circular plate is being heated so...

Question 11

Use Newton's Method to improve the given estimated solution to at least six significant digits.
-  $\mathrm{x}^{3}$ - $12=0 ; \mathrm{x}=2.4$

Accepted Answer

A)  2.28944 
B)  2.28942 
C)  2.34043 
D)  2.28943 
A)  2.28944 
B)  2.28942 
C)  2.34043 
D)  2.28943

Question 12

In the problems below, find any relative maximum or minimum values of each function.
- $y=x^{3}+2 x^{2}-7 x+4$

Accepted Answer

The answer of In the problems below, find any relative...

Question 13

Using a differential expression, find the percentage error in $V=\frac{4}{3} \pi r^{3}$ from $r=25.00$ in. to $25.10 \mathrm{in}$.

Accepted Answer

The answer of Using a differential expression, find the percentage...

Question 14

In the problems below, find any relative maximum or minimum values of each function.
-  $y=x^{4}-6 x^{2}+5$

Accepted Answer

The answer of In the problems below, find any relative...

Question 15

Given $y=5 x^{3}$ and $\frac{d x}{d t}=3$ at $x=2$, find $\frac{d y}{d t}$.

Accepted Answer

The answer of Given $y=5 x^{3}$ and $\frac{d x}{d t}=3$...

Question 16

Use Newton's Method to find a solution to six significant digits in the given interval.
-  $4 \sin x=\cos x ; 3 \leq x \leq 5$

Accepted Answer

The answer of Use Newton's Method to find a solution...

Question 17

Find dy for the expression $9 x^{2}+25 y^{2}=10$.

Accepted Answer

The answer of Find dy for the expression \(9 x^{2}+25...

Question 18

A cylinder with an inside radius of $35 \mathrm{~mm}$ is sealed at one end and a piston is at the other end. At what rate is the piston moving if fluid is being pumped into the cylinder at the rate of $60 \mathrm{~cm}^{3} / \mathrm{s}$ ? (Hint: Pay attention to units.)

Accepted Answer

The answer of A cylinder with an inside radius of...

Question 19

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the $\mathrm{x}$ - axis, symmetry, and asymptotes. Graph each equation.
-  $y^{2}=\frac{1}{x-3}$

Accepted Answer

None

Question 20

The power $P$ in watts (W) in a circuit with resistance $R$ in ohms $(\Omega)$ varies according to $\mathrm{P}=\frac{49 \mathrm{R}}{(\mathrm{R}+9)^{2}}$. Find the resistance that gives the maximum power.

Accepted Answer

The answer of The power $P$ in watts (W) in...

Find the relative maximum and minimum points of the function $f(x)=x^{3}-x^{2}+15 x+8$ .

Use Newton's Method to find a solution to six significant digits in the given interval. - $x^{4}-5 x^{2}-6=0 ; 2 \leq x \leq 4$

Name the horizontal and vertical asymptotes of the function $f(x)=\frac{3 x}{x^{2}-16}$ .

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the $\mathrm{x}$ - axis, symmetry, and asymptotes. Graph each equation. - $y=x^{3}-5 x^{2}-12 x+36$

Use Newton's Method to find a solution to six significant digits in the given interval. - $x^{3}-2 x^{2}=8 x-6 ; 3 \leq x \leq 5$

A rectangular box, open at the top, with a square base is to have a volume of $13,500 \mathrm{~cm}^{3}$ . Find the dimensions if the box is to contain the least amount of material.

The area of a square in terms of its diagonal $z$ is given by the formula $A=\frac{1}{2} z^{2}$ . Use a differential to estimate the change in the area of a square whose diagonal has been increased from $6.0 \mathrm{~cm}$ to 6.2 $\mathrm{cm}$ .

A circular plate is being heated so that its radius is increasing at a rate of $0.09 \mathrm{in}$ ./h. How fast is its area increasing when its radius is 15 inches?

Use Newton's Method to improve the given estimated solution to at least six significant digits. - $\mathrm{x}^{3}$ - $12=0 ; \mathrm{x}=2.4$

In the problems below, find any relative maximum or minimum values of each function. - $y=x^{3}+2 x^{2}-7 x+4$

Using a differential expression, find the percentage error in $V=\frac{4}{3} \pi r^{3}$ from $r=25.00$ in. to $25.10 \mathrm{in}$ .

In the problems below, find any relative maximum or minimum values of each function. - $y=x^{4}-6 x^{2}+5$

Given $y=5 x^{3}$ and $\frac{d x}{d t}=3$ at $x=2$ , find $\frac{d y}{d t}$ .

Use Newton's Method to find a solution to six significant digits in the given interval. - $4 \sin x=\cos x ; 3 \leq x \leq 5$

Find dy for the expression $9 x^{2}+25 y^{2}=10$ .

A cylinder with an inside radius of $35 \mathrm{~mm}$ is sealed at one end and a piston is at the other end. At what rate is the piston moving if fluid is being pumped into the cylinder at the rate of $60 \mathrm{~cm}^{3} / \mathrm{s}$ ? (Hint: Pay attention to units.)

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the $\mathrm{x}$ - axis, symmetry, and asymptotes. Graph each equation. - $y^{2}=\frac{1}{x-3}$

The power $P$ in watts (W) in a circuit with resistance $R$ in ohms $(\Omega)$ varies according to $\mathrm{P}=\frac{49 \mathrm{R}}{(\mathrm{R}+9)^{2}}$ . Find the resistance that gives the maximum power.

Analytic Geometry

The Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Exam 3: Applications of the Derivative

Find the relative maximum and minimum points of the function f(x)=x3−x2+15x+8f(x)=x^{3}-x^{2}+15 x+8f(x)=x3−x2+15x+8 .

Use Newton's Method to find a solution to six significant digits in the given interval. - x4−5x2−6=0;2≤x≤4x^{4}-5 x^{2}-6=0 ; 2 \leq x \leq 4x4−5x2−6=0;2≤x≤4

Name the horizontal and vertical asymptotes of the function f(x)=3xx2−16f(x)=\frac{3 x}{x^{2}-16}f(x)=x2−163x​ .

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the x\mathrm{x}x - axis, symmetry, and asymptotes. Graph each equation. - y=x3−5x2−12x+36y=x^{3}-5 x^{2}-12 x+36y=x3−5x2−12x+36

Use Newton's Method to find a solution to six significant digits in the given interval. - x3−2x2=8x−6;3≤x≤5x^{3}-2 x^{2}=8 x-6 ; 3 \leq x \leq 5x3−2x2=8x−6;3≤x≤5

A rectangular box, open at the top, with a square base is to have a volume of 13,500 cm313,500 \mathrm{~cm}^{3}13,500 cm3 . Find the dimensions if the box is to contain the least amount of material.

The area of a square in terms of its diagonal zzz is given by the formula A=12z2A=\frac{1}{2} z^{2}A=21​z2 . Use a differential to estimate the change in the area of a square whose diagonal has been increased from 6.0 cm6.0 \mathrm{~cm}6.0 cm to 6.2 cm\mathrm{cm}cm .

A circular plate is being heated so that its radius is increasing at a rate of 0.09in0.09 \mathrm{in}0.09in ./h. How fast is its area increasing when its radius is 15 inches?

Use Newton's Method to improve the given estimated solution to at least six significant digits. - x3\mathrm{x}^{3}x3 - 12=0;x=2.412=0 ; \mathrm{x}=2.412=0;x=2.4

In the problems below, find any relative maximum or minimum values of each function. - y=x3+2x2−7x+4y=x^{3}+2 x^{2}-7 x+4y=x3+2x2−7x+4

Using a differential expression, find the percentage error in V=43πr3V=\frac{4}{3} \pi r^{3}V=34​πr3 from r=25.00r=25.00r=25.00 in. to 25.10in25.10 \mathrm{in}25.10in .

In the problems below, find any relative maximum or minimum values of each function. - y=x4−6x2+5y=x^{4}-6 x^{2}+5y=x4−6x2+5

Given y=5x3y=5 x^{3}y=5x3 and dxdt=3\frac{d x}{d t}=3dtdx​=3 at x=2x=2x=2 , find dydt\frac{d y}{d t}dtdy​ .

Use Newton's Method to find a solution to six significant digits in the given interval. - 4sin⁡x=cos⁡x;3≤x≤54 \sin x=\cos x ; 3 \leq x \leq 54sinx=cosx;3≤x≤5

Find dy for the expression 9x2+25y2=109 x^{2}+25 y^{2}=109x2+25y2=10 .

A cylinder with an inside radius of 35 mm35 \mathrm{~mm}35 mm is sealed at one end and a piston is at the other end. At what rate is the piston moving if fluid is being pumped into the cylinder at the rate of 60 cm3/s60 \mathrm{~cm}^{3} / \mathrm{s}60 cm3/s ? (Hint: Pay attention to units.)

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the x\mathrm{x}x - axis, symmetry, and asymptotes. Graph each equation. - y2=1x−3y^{2}=\frac{1}{x-3}y2=x−31​

The power PPP in watts (W) in a circuit with resistance RRR in ohms (Ω)(\Omega)(Ω) varies according to P=49R(R+9)2\mathrm{P}=\frac{49 \mathrm{R}}{(\mathrm{R}+9)^{2}}P=(R+9)249R​ . Find the resistance that gives the maximum power.

Analytic Geometry

The Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Find the relative maximum and minimum points of the function $f(x)=x^{3}-x^{2}+15 x+8$ .

Use Newton's Method to find a solution to six significant digits in the given interval. - $x^{4}-5 x^{2}-6=0 ; 2 \leq x \leq 4$

Name the horizontal and vertical asymptotes of the function $f(x)=\frac{3 x}{x^{2}-16}$ .

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the $\mathrm{x}$ - axis, symmetry, and asymptotes. Graph each equation. - $y=x^{3}-5 x^{2}-12 x+36$

Use Newton's Method to find a solution to six significant digits in the given interval. - $x^{3}-2 x^{2}=8 x-6 ; 3 \leq x \leq 5$

A rectangular box, open at the top, with a square base is to have a volume of $13,500 \mathrm{~cm}^{3}$ . Find the dimensions if the box is to contain the least amount of material.

The area of a square in terms of its diagonal $z$ is given by the formula $A=\frac{1}{2} z^{2}$ . Use a differential to estimate the change in the area of a square whose diagonal has been increased from $6.0 \mathrm{~cm}$ to 6.2 $\mathrm{cm}$ .

A circular plate is being heated so that its radius is increasing at a rate of $0.09 \mathrm{in}$ ./h. How fast is its area increasing when its radius is 15 inches?

Use Newton's Method to improve the given estimated solution to at least six significant digits. - $\mathrm{x}^{3}$ - $12=0 ; \mathrm{x}=2.4$

In the problems below, find any relative maximum or minimum values of each function. - $y=x^{3}+2 x^{2}-7 x+4$

Using a differential expression, find the percentage error in $V=\frac{4}{3} \pi r^{3}$ from $r=25.00$ in. to $25.10 \mathrm{in}$ .

In the problems below, find any relative maximum or minimum values of each function. - $y=x^{4}-6 x^{2}+5$

Given $y=5 x^{3}$ and $\frac{d x}{d t}=3$ at $x=2$ , find $\frac{d y}{d t}$ .

Use Newton's Method to find a solution to six significant digits in the given interval. - $4 \sin x=\cos x ; 3 \leq x \leq 5$

Find dy for the expression $9 x^{2}+25 y^{2}=10$ .

A cylinder with an inside radius of $35 \mathrm{~mm}$ is sealed at one end and a piston is at the other end. At what rate is the piston moving if fluid is being pumped into the cylinder at the rate of $60 \mathrm{~cm}^{3} / \mathrm{s}$ ? (Hint: Pay attention to units.)

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the $\mathrm{x}$ - axis, symmetry, and asymptotes. Graph each equation. - $y^{2}=\frac{1}{x-3}$

The power $P$ in watts (W) in a circuit with resistance $R$ in ohms $(\Omega)$ varies according to $\mathrm{P}=\frac{49 \mathrm{R}}{(\mathrm{R}+9)^{2}}$ . Find the resistance that gives the maximum power.