Posted by Katia on .
find the intervals where the function is increasing and the intervals where it is decreasing
f(x)= (x^3/3)(x^2/2)
ok i found its derivative
which is (f1(x)=(x1)x
my options are increasing a) (0,infinity) b) (1,0) c(infinity,0)U(1,infinity)
decreasing a) (0,1) b) (infinity,0)U(1,infinity)
i cant seem to find the correct answers
because it is increasing from infinitive to 1. then increasing from 1,0 decreasing from 0,1 and increasing again from (1, infinity)
what im i doing wrong?

Calculus 
MathMate,
You have the correct calculations, but did not organize in a way that helps you get the right answer.
"because it is A(increasing from infinitive to 1). then B(increasing from 1,0), C(decreasing from 0,1)) and D(increasing again from (1, infinity))"
Statements A, B C and D are all correct.
Since A and B are both increasing, so can you not combine A and B?
Therefore you have two intervals that increase, and one single interval the decreases.
Post again if you still don't find the correct answer.