Exam 3: Differentiation Rules

A right circular cylinder is inscribed in a sphere of radius $r = 5 \mathrm {~cm}$ . Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.

(Multiple Choice)

4.9/5

(29)

Question 81

Estimate the extreme values of the function. Round the answers to the nearest hundredth. $y ( x ) = \frac { 1 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 40 x + 15$

(Short Answer)

4.8/5

(37)

Question 82

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r = 4$ . Select the correct answer.

(Multiple Choice)

4.8/5

(40)

Question 83

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r = 4$ .

(Multiple Choice)

4.8/5

(31)

Question 84

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r = 4$ . Select the correct answer.

(Multiple Choice)

4.9/5

(34)

Question 85

a) Graph the funtion $f ( x ) = x ^ { 2 } \ln x$ . b) Use l'Hospitals' rule to explain the behavior as $x \rightarrow 0$

(Short Answer)

4.8/5

(29)

Question 86

Find the local and absolute extreme values of the function on the given interval. $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x + 2 , \quad [ 2,4 ]$

(Short Answer)

4.9/5

(32)

Question 87

$\text { Find the intervals where } f ( x ) = \frac { \log 9 x } { x } \text { is increasing and where it is decreasing. }$

(Short Answer)

4.9/5

(36)

Question 88

How many points of inflection are on the graph of the function? $f ( x ) = 18 x ^ { 3 } + 5 x ^ { 2 } - 12 x - 20$ Select the correct answer.

(Multiple Choice)

4.7/5

(37)

Question 89

Use Newton's method to approximate the indicated root of $x ^ { 4 } + x - 4 = 0$ in the interval $[ 1,2 ]$ , correct to six decimal places. Use $x _ { 1 } = 1.5$ as the initial approximation.

(Short Answer)

4.7/5

(35)

Question 90

$\text { Find the critical number(s), if any, of the function } f ( x ) = e ^ { x ^ { 2 } - 10 x }$ Select the correct answer.

(Multiple Choice)

4.8/5

(31)

Question 91

Estimate the value of $\sqrt { 5 }$ by using three iterations of Newton's method to solve the equation $x ^ { 2 } - 5 = 0$ with initial estimate $x _ { 0 } = 2$ . Round your final estimate to four decimal places.

(Short Answer)

4.9/5

(33)

Question 92

$\text { What is the function of the graph? }$ $\text { What is the function of the graph? }$

(Short Answer)

4.7/5

(42)

Question 93

The function $f ( x ) = x ^ { 2 } - 6 x + 13$ satisfies the hypotheses of Rolle's Theorem on the interval $[ 0,6 ]$ . Find all values of $c$ that satisfy the conclusion of the theorem.

(Multiple Choice)

4.7/5

(45)

Question 94

Find the most general antiderivative of the function. $f ( x ) = 9 x ^ { 1 / 8 } - 11 x ^ { 1 / 10 }$

(Short Answer)

4.9/5

(35)

Question 95

$\text { Find the critical number(s), if any, of the function } f ( x ) = x ^ { 3 } - 21 x + 4 \text {. }$

(Short Answer)

4.9/5

(37)

Question 96

Determine where the graph of the function $f ( x ) = 3 + 4 x ^ { 1 / 3 }$ is concave upward and where it is concave downward. Also, find all inflection points of the function.

(Short Answer)

4.8/5

(37)

Question 97

Find all the critical numbers of the function. $g ( x ) = 7 x + \sin ( 7 x )$

(Short Answer)

4.7/5

(40)

Question 98

$\text { Use the Second Derivative Test to find the relative extrema, if any, of the function } f ( x ) = x + \frac { 64 } { x } \text {. }$ Select the correct answer.

(Multiple Choice)

4.9/5

(33)

Question 99

The graph of the derivative $f ^ { \prime } ( x )$ of a continuous function $\mathrm { f }$ is shown. On what intervals is $f$ decreasing? $The graph of the derivative f ^ { \prime } ( x ) of a continuous function \mathrm { f } is shown. On what intervals is f decreasing?$

(Short Answer)

4.9/5

(30)

Question 100

A right circular cylinder is inscribed in a sphere of radius $r = 5 \mathrm {~cm}$ . Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.

Estimate the extreme values of the function. Round the answers to the nearest hundredth. $y ( x ) = \frac { 1 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 40 x + 15$

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r = 4$ . Select the correct answer.

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r = 4$ .

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r = 4$ . Select the correct answer.

a) Graph the funtion $f ( x ) = x ^ { 2 } \ln x$ . b) Use l'Hospitals' rule to explain the behavior as $x \rightarrow 0$

Find the local and absolute extreme values of the function on the given interval. $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x + 2 , \quad [ 2,4 ]$

$\text { Find the intervals where } f ( x ) = \frac { \log 9 x } { x } \text { is increasing and where it is decreasing. }$

How many points of inflection are on the graph of the function? $f ( x ) = 18 x ^ { 3 } + 5 x ^ { 2 } - 12 x - 20$ Select the correct answer.

Use Newton's method to approximate the indicated root of $x ^ { 4 } + x - 4 = 0$ in the interval $[ 1,2 ]$ , correct to six decimal places. Use $x _ { 1 } = 1.5$ as the initial approximation.

$\text { Find the critical number(s), if any, of the function } f ( x ) = e ^ { x ^ { 2 } - 10 x }$ Select the correct answer.

Estimate the value of $\sqrt { 5 }$ by using three iterations of Newton's method to solve the equation $x ^ { 2 } - 5 = 0$ with initial estimate $x _ { 0 } = 2$ . Round your final estimate to four decimal places.

$\text { What is the function of the graph? }$ $\text { What is the function of the graph? }$

The function $f ( x ) = x ^ { 2 } - 6 x + 13$ satisfies the hypotheses of Rolle's Theorem on the interval $[ 0,6 ]$ . Find all values of $c$ that satisfy the conclusion of the theorem.

Find the most general antiderivative of the function. $f ( x ) = 9 x ^ { 1 / 8 } - 11 x ^ { 1 / 10 }$

$\text { Find the critical number(s), if any, of the function } f ( x ) = x ^ { 3 } - 21 x + 4 \text {. }$

Determine where the graph of the function $f ( x ) = 3 + 4 x ^ { 1 / 3 }$ is concave upward and where it is concave downward. Also, find all inflection points of the function.

Find all the critical numbers of the function. $g ( x ) = 7 x + \sin ( 7 x )$

$\text { Use the Second Derivative Test to find the relative extrema, if any, of the function } f ( x ) = x + \frac { 64 } { x } \text {. }$ Select the correct answer.

The graph of the derivative $f ^ { \prime } ( x )$ of a continuous function $\mathrm { f }$ is shown. On what intervals is $f$ decreasing? $The graph of the derivative f ^ { \prime } ( x ) of a continuous function \mathrm { f } is shown. On what intervals is f decreasing?$

Functions and Models

Limits and Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

Exam 3: Differentiation Rules

A right circular cylinder is inscribed in a sphere of radius r=5 cmr = 5 \mathrm {~cm}r=5 cm . Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.

Estimate the extreme values of the function. Round the answers to the nearest hundredth. y(x)=13x3−7x2+40x+15y ( x ) = \frac { 1 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 40 x + 15y(x)=31​x3−7x2+40x+15

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius r=4r = 4r=4 . Select the correct answer.

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius r=4r = 4r=4 .

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius r=4r = 4r=4 . Select the correct answer.

a) Graph the funtion f(x)=x2ln⁡xf ( x ) = x ^ { 2 } \ln xf(x)=x2lnx . b) Use l'Hospitals' rule to explain the behavior as x→0x \rightarrow 0x→0

Find the local and absolute extreme values of the function on the given interval. f(x)=x3−6x2+9x+2,[2,4]f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x + 2 , \quad [ 2,4 ]f(x)=x3−6x2+9x+2,[2,4]

Find the intervals where f(x)=log⁡9xx is increasing and where it is decreasing. \text { Find the intervals where } f ( x ) = \frac { \log 9 x } { x } \text { is increasing and where it is decreasing. } Find the intervals where f(x)=xlog9x​ is increasing and where it is decreasing.

How many points of inflection are on the graph of the function? f(x)=18x3+5x2−12x−20f ( x ) = 18 x ^ { 3 } + 5 x ^ { 2 } - 12 x - 20f(x)=18x3+5x2−12x−20 Select the correct answer.

Use Newton's method to approximate the indicated root of x4+x−4=0x ^ { 4 } + x - 4 = 0x4+x−4=0 in the interval [1,2][ 1,2 ][1,2] , correct to six decimal places. Use x1=1.5x _ { 1 } = 1.5x1​=1.5 as the initial approximation.

Find the critical number(s), if any, of the function f(x)=ex2−10x\text { Find the critical number(s), if any, of the function } f ( x ) = e ^ { x ^ { 2 } - 10 x } Find the critical number(s), if any, of the function f(x)=ex2−10x Select the correct answer.

Estimate the value of 5\sqrt { 5 }5​ by using three iterations of Newton's method to solve the equation x2−5=0x ^ { 2 } - 5 = 0x2−5=0 with initial estimate x0=2x _ { 0 } = 2x0​=2 . Round your final estimate to four decimal places.

What is the function of the graph? \text { What is the function of the graph? } What is the function of the graph?

The function f(x)=x2−6x+13f ( x ) = x ^ { 2 } - 6 x + 13f(x)=x2−6x+13 satisfies the hypotheses of Rolle's Theorem on the interval [0,6][ 0,6 ][0,6] . Find all values of ccc that satisfy the conclusion of the theorem.

Find the most general antiderivative of the function. f(x)=9x1/8−11x1/10f ( x ) = 9 x ^ { 1 / 8 } - 11 x ^ { 1 / 10 }f(x)=9x1/8−11x1/10

Find the critical number(s), if any, of the function f(x)=x3−21x+4. \text { Find the critical number(s), if any, of the function } f ( x ) = x ^ { 3 } - 21 x + 4 \text {. } Find the critical number(s), if any, of the function f(x)=x3−21x+4.

Determine where the graph of the function f(x)=3+4x1/3f ( x ) = 3 + 4 x ^ { 1 / 3 }f(x)=3+4x1/3 is concave upward and where it is concave downward. Also, find all inflection points of the function.

Find all the critical numbers of the function. g(x)=7x+sin⁡(7x)g ( x ) = 7 x + \sin ( 7 x )g(x)=7x+sin(7x)

The graph of the derivative f′(x)f ^ { \prime } ( x )f′(x) of a continuous function f\mathrm { f }f is shown. On what intervals is fff decreasing?

Functions and Models

Limits and Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

A right circular cylinder is inscribed in a sphere of radius $r = 5 \mathrm {~cm}$ . Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.

Estimate the extreme values of the function. Round the answers to the nearest hundredth. $y ( x ) = \frac { 1 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 40 x + 15$

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r = 4$ . Select the correct answer.

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r = 4$ .

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r = 4$ . Select the correct answer.

a) Graph the funtion $f ( x ) = x ^ { 2 } \ln x$ . b) Use l'Hospitals' rule to explain the behavior as $x \rightarrow 0$

Find the local and absolute extreme values of the function on the given interval. $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x + 2 , \quad [ 2,4 ]$

$\text { Find the intervals where } f ( x ) = \frac { \log 9 x } { x } \text { is increasing and where it is decreasing. }$

How many points of inflection are on the graph of the function? $f ( x ) = 18 x ^ { 3 } + 5 x ^ { 2 } - 12 x - 20$ Select the correct answer.

Use Newton's method to approximate the indicated root of $x ^ { 4 } + x - 4 = 0$ in the interval $[ 1,2 ]$ , correct to six decimal places. Use $x _ { 1 } = 1.5$ as the initial approximation.

$\text { Find the critical number(s), if any, of the function } f ( x ) = e ^ { x ^ { 2 } - 10 x }$ Select the correct answer.

Estimate the value of $\sqrt { 5 }$ by using three iterations of Newton's method to solve the equation $x ^ { 2 } - 5 = 0$ with initial estimate $x _ { 0 } = 2$ . Round your final estimate to four decimal places.

$\text { What is the function of the graph? }$ $\text { What is the function of the graph? }$

The function $f ( x ) = x ^ { 2 } - 6 x + 13$ satisfies the hypotheses of Rolle's Theorem on the interval $[ 0,6 ]$ . Find all values of $c$ that satisfy the conclusion of the theorem.

Find the most general antiderivative of the function. $f ( x ) = 9 x ^ { 1 / 8 } - 11 x ^ { 1 / 10 }$

$\text { Find the critical number(s), if any, of the function } f ( x ) = x ^ { 3 } - 21 x + 4 \text {. }$

Determine where the graph of the function $f ( x ) = 3 + 4 x ^ { 1 / 3 }$ is concave upward and where it is concave downward. Also, find all inflection points of the function.

Find all the critical numbers of the function. $g ( x ) = 7 x + \sin ( 7 x )$

The graph of the derivative $f ^ { \prime } ( x )$ of a continuous function $\mathrm { f }$ is shown. On what intervals is $f$ decreasing? $The graph of the derivative f ^ { \prime } ( x ) of a continuous function \mathrm { f } is shown. On what intervals is f decreasing?$