Im having a problem with curve sketching i cant figure out how to do this problem. I am confused.(adsbygoogle = window.adsbygoogle || []).push({});

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 doesnt 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 dont know how to determine the intervals of decrease or increase because of i, so can you please help me.

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