 # Calculus Help: Analyzing Graphs Anonymous
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.

## Tutor Answer

KatS
School: Carnegie Mellon University   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  Review Anonymous
Top quality work from this guy! I'll be back! 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