Question 1

Determine the slant asymptote of the graph of $$f ( x ) = \frac { 5 x ^ { 2 } - 9 x + 5 } { x - 1 }$$

Accepted Answer

A)  $y = 5 x + 4$ 
B)  $y = 5 x - 4$ 
C)  $y = - 5 x - 4$ 
D)  $y = - 5 x + 4$ 
E)  no slant asymptotes 
A)  $y = 5 x + 4$ 
B)  $y = 5 x - 4$ 
C)  $y = - 5 x - 4$ 
D)  $y = - 5 x + 4$ 
E)  no slant asymptotes

Question 2

Find the points of inflection and discuss the concavity of the function $f ( x ) = - \sin x + \cos x \text { on the interval } ( 0,2 \pi )$ .

Accepted Answer

A)  no inflection points. concave up on $( 0,2 \pi )$ 
B)  concave upward on $\left( 0 , \frac { 1 } { 2 } \pi \right)$; concave downward on $\left( \frac { 5 } { 2 } \pi , 2 \pi \right)$; inflection point at $\left( 0 , \frac { 1 } { 2 } \pi \right)$ 
C)  no inflection points. concave down on $( 0,2 \pi )$ 
D)  concave downward on $\left( 0 , \frac { 1 } { 2 } \pi \right)$; concave upward on $\left( \frac { 5 } { 2 } \pi , 2 \pi \right)$; inflection point at $\left( 0 , \frac { 1 } { 2 } \pi \right)$ 
E)  none of the above 
A)  no inflection points. concave up on $( 0,2 \pi )$ 
B)  concave upward on $\left( 0 , \frac { 1 } { 2 } \pi \right)$; concave downward on $\left( \frac { 5 } { 2 } \pi , 2 \pi \right)$; inflection point at $\left( 0 , \frac { 1 } { 2 } \pi \right)$ 
C)  no inflection points. concave down on $( 0,2 \pi )$ 
D)  concave downward on $\left( 0 , \frac { 1 } { 2 } \pi \right)$; concave upward on $\left( \frac { 5 } { 2 } \pi , 2 \pi \right)$; inflection point at $\left( 0 , \frac { 1 } { 2 } \pi \right)$ 
E)  none of the above

Question 3

Find the point on the graph of the function $f ( x ) = \sqrt { x } \text { that is closest to the }$ point $( 18,0 )$

Accepted Answer

A)  $\left( \frac { 35 } { 2 } , \sqrt { \frac { 35 } { 2 } } \right)$ 
B)  $\left( \frac { 37 } { 2 } , \sqrt { \frac { 37 } { 2 } } \right)$ 
C)  $\left( \frac { 35 } { 2 } , \sqrt { \frac { 37 } { 2 } } \right)$ 
D)  $\left( \sqrt { \frac { 37 } { 2 } } , \frac { 35 } { 2 } \right)$ 
E)  $\left( \sqrt { \frac { 35 } { 2 } } , \frac { 35 } { 2 } \right)$ 
A)  $\left( \frac { 35 } { 2 } , \sqrt { \frac { 35 } { 2 } } \right)$ 
B)  $\left( \frac { 37 } { 2 } , \sqrt { \frac { 37 } { 2 } } \right)$ 
C)  $\left( \frac { 35 } { 2 } , \sqrt { \frac { 37 } { 2 } } \right)$ 
D)  $\left( \sqrt { \frac { 37 } { 2 } } , \frac { 35 } { 2 } \right)$ 
E)  $\left( \sqrt { \frac { 35 } { 2 } } , \frac { 35 } { 2 } \right)$

Question 4

Find all points of inflection, if any exist, of the graph of the function $f ( x ) = x \sqrt { x + 3 }$. Round your answers to two decimal places.

Accepted Answer

A)  $( 6,18 )$ 
B)  $( 1,2 ) , ( 3,7.35 )$ 
C)  $( 1,2 ) , ( 2,4.47 )$ 
D)  $( 3,7.35 )$ 
E)  no points of inflection 
A)  $( 6,18 )$ 
B)  $( 1,2 ) , ( 3,7.35 )$ 
C)  $( 1,2 ) , ( 2,4.47 )$ 
D)  $( 3,7.35 )$ 
E)  no points of inflection

Question 5

The graph of f is shown below. For which value of x is $f ^ { t } ( x ) \text { minimum? }$

Accepted Answer

A)  $x = 4$ 
B)  $x = 2$ 
C)  $x = 0$ 
D)  $x = - 2$ 
E)  $x = 6$ 
A)  $x = 4$ 
B)  $x = 2$ 
C)  $x = 0$ 
D)  $x = - 2$ 
E)  $x = 6$

Question 6

Use a computer algebra system to graph the function $\frac { 4 } { 3 } x \sqrt { 3 - x } \text { and determine all }$ absolute extrema on the interval $[ 0,3 ]$

Accepted Answer

A)  absolute maximum: $\left( 2 , \frac { 8 } { 3 } \right)$ absolute minimum: $( 0,0 ) ( 3,0 )$ 
B)  absolute maximum: $\left( 1 , \frac { 4 } { 3 } \right)$ absolute minimum: $( 0,0 ) ( 3,0 )$ 
C)  absolute maximum: $( 3,4 )$ absolute minimum: $( 0,0 )$ 
D)  absolute maximum: $( 3,4 )$ absolute minimum: $( 0,3 )$ 
E)  absolute maximum: $\left( 2 , \frac { 8 } { 3 } \right)$ absolute minimum: $( 0,3 )$ 
A)  absolute maximum: $\left( 2 , \frac { 8 } { 3 } \right)$ absolute minimum: $( 0,0 ) ( 3,0 )$ 
B)  absolute maximum: $\left( 1 , \frac { 4 } { 3 } \right)$ absolute minimum: $( 0,0 ) ( 3,0 )$ 
C)  absolute maximum: $( 3,4 )$ absolute minimum: $( 0,0 )$ 
D)  absolute maximum: $( 3,4 )$ absolute minimum: $( 0,3 )$ 
E)  absolute maximum: $\left( 2 , \frac { 8 } { 3 } \right)$ absolute minimum: $( 0,3 )$

Question 7

$\text { Compare } d y \text { and } \Delta y \text { for } y = 2 x ^ { 4 } + 1 \text { at } x = 0 \text { with } \Delta x = d x = 0.02 \text {. Give your }$ answers to four decimal places.

Accepted Answer

A)  $d y = - 0.0300 ; \Delta y = - 0.0003$ 
B)  $d y = 0.0200 ; \Delta y = - 0.0001$ 
C)  $d y = 0.0000 ; \Delta y = 0.0000$ 
D)  $d y = - 0.0100 ; \Delta y = - 0.0002$ 
E)  $d y = - 0.0300 ; \Delta y = - 0.0001$ 
A)  $d y = - 0.0300 ; \Delta y = - 0.0003$ 
B)  $d y = 0.0200 ; \Delta y = - 0.0001$ 
C)  $d y = 0.0000 ; \Delta y = 0.0000$ 
D)  $d y = - 0.0100 ; \Delta y = - 0.0002$ 
E)  $d y = - 0.0300 ; \Delta y = - 0.0001$

Determine the slant asymptote of the graph of $f ( x ) = \frac { 5 x ^ { 2 } - 9 x + 5 } { x - 1 }$

Find the points of inflection and discuss the concavity of the function $f ( x ) = - \sin x + \cos x \text { on the interval } ( 0,2 \pi )$ .

Find the point on the graph of the function $f ( x ) = \sqrt { x } \text { that is closest to the }$ point $( 18,0 )$

Find all points of inflection, if any exist, of the graph of the function $f ( x ) = x \sqrt { x + 3 }$ . Round your answers to two decimal places.

The graph of f is shown below. For which value of x is $f ^ { t } ( x ) \text { minimum? }$ $The graph of f is shown below. For which value of x is f ^ { t } ( x ) \text { minimum? }$

Use a computer algebra system to graph the function $\frac { 4 } { 3 } x \sqrt { 3 - x } \text { and determine all }$ absolute extrema on the interval $[ 0,3 ]$

$\text { Compare } d y \text { and } \Delta y \text { for } y = 2 x ^ { 4 } + 1 \text { at } x = 0 \text { with } \Delta x = d x = 0.02 \text {. Give your }$ answers to four decimal places.

Graphs and Models

A Preview of Calculus

The Derivative and the Tangent Line Problem

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Exam 4: Extrema on an Interval

Determine the slant asymptote of the graph of f(x)=5x2−9x+5x−1f ( x ) = \frac { 5 x ^ { 2 } - 9 x + 5 } { x - 1 }f(x)=x−15x2−9x+5​

Find the points of inflection and discuss the concavity of the function f(x)=−sin⁡x+cos⁡x on the interval (0,2π)f ( x ) = - \sin x + \cos x \text { on the interval } ( 0,2 \pi )f(x)=−sinx+cosx on the interval (0,2π) .

Find the point on the graph of the function f(x)=x that is closest to the f ( x ) = \sqrt { x } \text { that is closest to the }f(x)=x​ that is closest to the point (18,0)( 18,0 )(18,0)

Find all points of inflection, if any exist, of the graph of the function f(x)=xx+3f ( x ) = x \sqrt { x + 3 }f(x)=xx+3​ . Round your answers to two decimal places.

The graph of f is shown below. For which value of x is ft(x) minimum? f ^ { t } ( x ) \text { minimum? }ft(x) minimum?

Use a computer algebra system to graph the function 43x3−x and determine all \frac { 4 } { 3 } x \sqrt { 3 - x } \text { and determine all }34​x3−x​ and determine all absolute extrema on the interval [0,3][ 0,3 ][0,3]

Graphs and Models

A Preview of Calculus

The Derivative and the Tangent Line Problem

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Determine the slant asymptote of the graph of $f ( x ) = \frac { 5 x ^ { 2 } - 9 x + 5 } { x - 1 }$

Find the points of inflection and discuss the concavity of the function $f ( x ) = - \sin x + \cos x \text { on the interval } ( 0,2 \pi )$ .

Find the point on the graph of the function $f ( x ) = \sqrt { x } \text { that is closest to the }$ point $( 18,0 )$

Find all points of inflection, if any exist, of the graph of the function $f ( x ) = x \sqrt { x + 3 }$ . Round your answers to two decimal places.

The graph of f is shown below. For which value of x is $f ^ { t } ( x ) \text { minimum? }$ $The graph of f is shown below. For which value of x is f ^ { t } ( x ) \text { minimum? }$

Use a computer algebra system to graph the function $\frac { 4 } { 3 } x \sqrt { 3 - x } \text { and determine all }$ absolute extrema on the interval $[ 0,3 ]$