- #1
F.B
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Im having a problem with curve sketching i can't figure out how to do this problem. I am confused.
Heres the question
1. For the following curve find:
a)the domain
b)the intercepts
c)the asymptotes
d)intervals of increase or decrease: local maximum and minimum
e)concavity and the point of inflection
x^2 - x - 1 / x-1
Heres my work.
a) the domain is x = 1
b)Let y=0
y = 0 - 0 - 1/ 0-1
y=1
Let x = 0
x^2 - x - 1 = 0
x = 1.62 or x = 0.62
c) Vertical asymptote:
x = 1
Horizontal asymptote
x^2 - x - 1 / x-1
y = x - 1/ x-1
Therefore it has an slant asympote at y = x
Heres where it gets fun
d) y = x^2 - x - 1/x-1
y'= x^2 - 2x + 2/ (x-1)^2
let y'= 0
x^2 - 2x - 2 = 0
x = 1 +/- i
Do i say that it doesn't have an maximum or minimum point because they are
imaginary?
e) y'' = -2/(x-1)^3
Let y''=0
-2 cannot equal 0
So there are no points of inflection, but then how do i determine the
concavity when my first derivative is based on imaginary numbers.
I have never encountered one like this. I don't know how to determine the intervals of decrease or increase because of i, so can you please help me.
Heres the question
1. For the following curve find:
a)the domain
b)the intercepts
c)the asymptotes
d)intervals of increase or decrease: local maximum and minimum
e)concavity and the point of inflection
x^2 - x - 1 / x-1
Heres my work.
a) the domain is x = 1
b)Let y=0
y = 0 - 0 - 1/ 0-1
y=1
Let x = 0
x^2 - x - 1 = 0
x = 1.62 or x = 0.62
c) Vertical asymptote:
x = 1
Horizontal asymptote
x^2 - x - 1 / x-1
y = x - 1/ x-1
Therefore it has an slant asympote at y = x
Heres where it gets fun
d) y = x^2 - x - 1/x-1
y'= x^2 - 2x + 2/ (x-1)^2
let y'= 0
x^2 - 2x - 2 = 0
x = 1 +/- i
Do i say that it doesn't have an maximum or minimum point because they are
imaginary?
e) y'' = -2/(x-1)^3
Let y''=0
-2 cannot equal 0
So there are no points of inflection, but then how do i determine the
concavity when my first derivative is based on imaginary numbers.
I have never encountered one like this. I don't know how to determine the intervals of decrease or increase because of i, so can you please help me.