Question

Analyze the graph of y= x^3 -3x +2 by finding the required information.

Answer 1

first find y'
can you do that?

Answer 2

Yes, I already found them all, but some of them got wrong so I am correcting, I just don't which ones specifically I got wrong. Can you help with that? my y- intercepts I got (0,2)

Answer 3

yes thats correct for y intecept

y = 2 when x = 0

Answer 4

y' = 3x^2 - 3
3x^2 - 3 = 0 at turning points on the graph
3x^2 = 3
x^2 = 1
and x = +1 , -1

so you have truning points at x = 1 and x = -1

Answer 5

do you know how to find the nature of these turning points?

Answer 6

Ok, that one I got wrong, I had 0,1 . Then I have no vertical or horizontal asymptotes. For increasing intervals I have ( -1, 0) , decreasing intervals ( 0,3) I think I got that one wrong. Then relative maxima (0,2), and relative minima (1,0) ?

Answer 7

do they want you to determine the max and min by finding increasing / decreasing intervals?
y

Answer 8

Well, I first found the relatives max and min, then the increasing and decreasing intervals, followed by the inflection points and finally the convape up and down intervals... however, I think I got the increasing and decreasing int. completely wrong?

Answer 9

darn it i just lost my post (how i dont know)

Answer 10

relative maximums is at (-1,4) and relative minimum is at (1,0)

Answer 11

ignore my 3rd last post - I messed up!!
I've tried to delete it but the system wont let me.

Answer 12

Yeah, hate it when that happens :) Oh, ok, so the max I got wrong. Uh, my concave up intervals are ( - infinity, - 1/2) , ( 1/2, +infinity) ; cocave down ( -1/2, 1/2) . My inflection points are 6,0

Answer 13

ok

Answer 14

geez i must admit i've forgotten how to do those concave up and down turning points

Answer 15

have you found the zeroes of the function or dont they want those?

Answer 16

as there is a minimum at the point (1,0) that is also a zero of the function

Answer 17

No, I haven't found the zeros

Answer 18

x^3 - 3x + 2 = 0

there must bea xero < -1 where there's a maximum

try -2:

(-2)^3 - 3(-2) + 2 = 0

ok theres a zero at (-2,0) and and at (1,0) as I explained above

Answer 19

the graph will lokk a bit like