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is it 4y^3... ??

how did you get that >?

yes its 4y^3

is the equation of the curve "4y^3 +2y -6" ? or is that the 1st derivative of it?

thats the first derivative..the eqauation of the porabola is x-y^2=0

yes i can figure the rest out .. its the factoring that for some reason is hurting me ...

factor a 2:
2(2y^3 +y -3) = 0
2y^3 +y -3 = 0 is easier to play with

we could use long division to try it, but synthetic division is more compact....

(y-1) (2y^2 +2y +3)

the quad facotrs easily now right?

which means, there there is only one critical point; and it is at y=1

any of that make sense?

makes perfect sense.. thanks you much ...

youre welcome :)