Thread: Intervals

For y=(1/4)x^4-(2/3)x^3+(1/2)x^2-3 find the exact intervals on which the function is:

a) increasing
b) decreasing
c) concave up
d) concave down
Then find any
e) local extreme values
f) inflection points

I graphed this and came up with the following answers:

a) (0, infinity)
b) ( -infinity, 0)
c) (-infinity, infinity)
d) none
e) Min: -3 at x=0
Max: none
f) none

Does that look right?

aren't you supposed to use information from the first and second derivatives to analyze the function, rather than just looking at a graph?

Ok so x^3-2x^2+x would be the first derivative...

and the second one would be 3x^2-4x+1 ?

I still don't know how to do it without graphing...but I guess I could graph those two?

have you learned about the first and second derivative tests and what they can tell you about a function?