Question

For the following equation do the following:
a) find f'(x) and an accompanying sign analysis (show increasing/decreasing)
b) the coordinates of any relative extrema
c) f''(x) and an accompanying sign analysis (show concave up/down)
d) the coordinates of any inflection points
e) the coordinates of all x and y intercepts (i do not need you to do this for me)
f) the equations of all asymptotes
g) an accurate sketch of the graph (i do not need you to do this for me)

f(x)=x^4+2x^3-3x^2-4x+4

... I !#$*ING HATE THIS QUESTION >_<"

Answer 1

well what have you got for f'(x) ?

Answer 2

2(x+2)(x-1)(2x-1)

Answer 3

You know, I think it's hard to put all the answers for this, we need a table of sorts :D

Answer 4

yeah these are just long a painful
first thing is to mark the zero's, because that tells us where the sign is changing

Answer 5

so set\[f'(x)=0\]and you will get a set of intervals between each zero

Answer 6

test a point in each interval and see if in that interval f' is >0 or <0
f'>0 means increasing
f'<0 means decreasing

Answer 7

I think I got it, thanks for the help! (: if you want you can check over what i did to see if i got the right idea:

to find f'(x) i used synthetic division and got x2+4x+4, then i factored it so i could do the sign analysis and got 2(x+2)(x-1)(2x-1)
Increase - (-2, 1/2)U(1,infinity)
Decrease - (-infinity, -2)U(1/2,1)

To find f''(x) i simply used product rule (f'gh+fg'h+fgh') and got (2x-1)(2x+4) and did sign analysis
Concave up - (-infinity,-1/2)U(1/2,infinity)
Concave down - (-1/2, 1/2)

... of course this is trying to compress 3/4 pages of work into a post, but i think you get the general idea.