Funtion f and derivatives Help please...

[phawksbball24]

Consider the function f, whose formula and derivatives are given below:

f(x)=(2x^2-5x+5)/x-2
f'(x)=(2x^2-8x+5)/(x-2)^2
f''(x)=6/(x-2)^3

a) Find and describe all of the vertical, horizontal, and slant asymptotes of this function, if any.

b) Find all of the roots of these functions, if any.

c) Find all of the local extrema of this function, if any.

d) Find all of the inflection points of this function, if any.

e) Sketch this function, including all of the features above in your sketch


I am totally lost and I am not sure where to start. The slant asymptote is especially where I get lost. Any of your help would be appreciated thank you.

 

[phawksbball24]

so do i find the derivative of the y=x line? because that just equals 1 and i dont know how to use that

 

[wind]

I'll try to help but you might want someone to check this over

Find and describe all of the vertical, horizontal, and slant asymptotes of this function, if any.

the verticle asymptoes are the domain restrictions of the original function

f(x)=(2x^2-5x+5)/x-2

this function will not have horizontal asymptoes because the higherst power of x is not on the bottom.

oblique asymptoes- use long division

Find all of the local extrema of this function, if any.

f'(x)=(2x^2-8x+5)/(x-2)^2

set the first derivitive to 0

0=(2x^2-8x+5)

solve, those are the possible max or min values. use the second derivitive test to see if they r max or min.

if the 2nd derivitive is pos, then it is concave up and a min value
if the 2nd derivitive is neg, then it is concave down and a max value

Find all of the inflection points of this function, if any.

set the second derivitive to 0
f''(x)=6/(x-2)^3
0=6

no points of inflection

you can use this software to check ur solution

http://www.download.com/DeadLine/3000-2053_4-10615891.html?tag=lst-0-1[/url]

 

[phawksbball24]

thanks that helped a lot but im still a little confused about how to use long division to find oblique asymptotes?

 

[wind]

http://www.purplemath.com/modules/asymtote3.htm


use this as an example, that program will also find the local extream so u can make sure ur answer is correct

set the second derivitive to 0
f''(x)=6/(x-2)^3
0=6
no points of inflection

I'm not really sure about this part...