# Calculus Help: Analyzing Graphs

*label*Mathematics

*timer*Asked: Mar 8th, 2019

*account_balance_wallet*$9.99

### Question Description

There is a total of three questions that I need help with. They all pertain to analyzing the graphs given. Each question has 5 parts, but some parts may not need to be completed depending on the question. Please let me know if you have any questions or need any pages from my textbook. All questions are on the word doc provided.

### Unformatted Attachment Preview

Purchase answer to see full attachment

## Tutor Answer

Attached. Please just reply if you have any questions.

1.

Correct sketch: upper left.

a. x intercept: set y = 0 and solve for x

0 = x^2 + x^-2

DNE

y intercept: set x = 0 and solve for y.

y = 0^2 + 1/0^2

DNE

x int (x,y) = DNE

y int (x,y) = DNE

b. To find extrema, take the derivative, set equal to zero to find the critical points.

−3

y ' = 2x− 2x

2

0= 2x− 3

x

2

= 2x

3

x

4

2= 2x

4

1= x

x= ± 1

You can then use the first derivative test to determine what type of extrema this is.

Pick points on either side to determine if the function is increasing or decreasing. Remember to

also divide the interval at vertical asymptotes (x = 0)

(-inf, -1) f ' (-2) = -3.75 DECREASING

(-1, 0) f ' ( -0.5) = 15

INCREASING

(0, 1) f ' (0.5) = -15

DECREASING

(1, inf) f ' (2) = 3.75

INCREASING

At x = -1, the function goes from decreasing to increasing making that a local minimum

At x = 1, the function goes from decreasing to increasing making that a local minimum

relative minimum (x,y) = (-1,2)

relative minimum (x,y) = (1,2)

c. To find possible inflection points, find the second derivative and set that equal to zero.

−4

y ' ' = 2+ 6x

6

0= 2+ 4

x

6

− 2= 4

x

4

− 2x = 6

4

x =− 3

NO SOLUTION

Since you cannot take the even root of a negative number, there will be no solution. Therefore

there can be no inflection points.

(x,y) = DNE

d. First determine where the original function is undefined. This will be where the

denominator is equal to zero. That point is when x = 0.

Then determine how the function behaves as you get closer and closer to zero. You can do this

by plugging a few values in for x.

y(0.5) = 4.25

y(0.1) = 100.01

y(0.01) = 10000.0001

You can see from that, as x gets closer to zero, the function is getting much larger.

We could have also looked at the first derivative from part b. In the 2 intervals approaching 0

from the left and right. From the left the function is increasing, going toward infinity. From the

right going from x = 0 to x = 1, the function is decreasing that means that moving back toward 0

it would be increasing.

Y → + infinity, as x →...

*flag*Report DMCA

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors