Question

*consider the function f(x)=x^2 -1 / x^3

a) Find the horizntal and vertical asymptotes.

b) what are the critical points of the function.

c) on what intervals is the function increasing and decreasing.

d) At what points, if any, does the function assume local extreme values.

e) Determine the conavity of the function's curve, and find the inflection points.

Answer 1

1. To find the horiz asy, take the limit of f(x) as x approaches infinity.
Alternatively, notice that the order of the numerator of your f(x) is 2 and that of the denominator is 3. Does that tell you anything about the limit of f(x) as s approaches infinity?
2. To find the vert. asy., take the denom. and set it equal to zero. Solve for x.

Your result (written as an equation, x = ? ), will represent the vertical asy.

Have you found vert. and horiz. asy. before?

Answer 2

no I'm not found before ..

Answer 3

I want example ..

Answer 4

@loser66
can you help me ?

Answer 5

It' s need a lot of patience and time (which I don't have right now),
let's try, I don't teach you, just ask you to do some thing and make sure you quickly reply, ok? need your patience, too.
at the few first step, it will sound like I say something......crazy. be patient, ok?

Answer 6

when x =0, y=?

Answer 7

ammm y=0

Answer 8

nope, at the denominator, it says x = 0 , y is undefined --> vertical asymptote is x =0 (or y axis)

Answer 9

I don't understand :(

Answer 10

in other words, let the denominator =0 , solve for x , that x give you vertical asymptote
now, make some values of y to make it clear
x =-2, y = -3/8
x=-1, y =0
x =0, y undefined
x = 1, y = 0
x= 2, y = 3/8