Find intervals on which function is (a) increasing (b) decreasing (c) concave up (d) concave down (e) local extreme values (f) inflextion points of:
The Attempt at a Solution
(a) To find where function is increasing, I tried using f'>0
Y' = 1-2x-4x3
So 1-2x-4x3>0 yields:
So x= 1/2 and 0
But the answer in the back of the book says (-infinity, 0.385)
(b) So decreasing is f'<0 and I did the same thing as (a) except with the sign that was different. The answer was [0.385, infinity) but again - my work didn't correspond to the answer! I have no idea how they got it.
(c) For concave up, it's f">0
I solved it and got x2<-1/6
Since it's a negative, it's no solution so the answer is None.
(d) Same thing except it's now f"<0
The answer in the back of the book said (-infinity, infinity) ----- but where did they get this?
(e) Local extreme values, found when f'=0 (aka: critical points)
I get x=1/2 but.. the answer in the back said local max was at (0.385, 1.215)
(f) Inflextion points is at f"=0
Got x^2 = -1/6 so it's none.
What am I doing wrong? How come my work isnt' close to the correct answer? D: