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## Homework Statement

Find intervals on which function is (a) increasing (b) decreasing (c) concave up (d) concave down (e) local extreme values (f) inflextion points of:

Y=1+x-x

^{2}-x

^{4}

## Homework Equations

Y=1+x-x

^{2}-x

^{4}

## The Attempt at a Solution

(a) To find where function is increasing, I tried using f'>0

Y' = 1-2x-4x

^{3}

So 1-2x-4x

^{3}>0 yields:

1>2x(1+2x

^{2})

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 x

^{2}<-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: