Increasing/decreasing intervals, concavity, totally not getting this problem?

Hi,

Ok, so here's my problem. I'm supposed to find the intervals on which this function is increasing / decreasing.

f(x) = 2x^2 - 8(x^4)

That gives me

f'(x) = 4x - 32x^3

So to find x, I set it to equal 0.

0 = 4x - 32x^3

0 = 4x(1 - 8x^2)

Which gives me

4x = 0

and

1 - 8x^2 = 0

===>

x = 0

and

1 = 8x^2

1/8 = x^2

x = (positive and negative) sqrt(1/8)

So I got x = 0, (positive and negative) sqrt(1/8)

(Typing "infinity" as "INF" and "-infinity" as "-INF") that gives me these intervals:

(-INF, -(sqrt(1/8)))

(-(sqrt(1/8)), 0)

(0, (sqrt(1/8)))

((sqrt(1/8)), INF)

So I set up a little chart.

Headings for the column are as such:

Interval | 4x | (1-8x^2) | f'(x) | f is...

First column, I write the interval;

Second column, I write whether plugging in a number from said interval into 4x will give me a positive or negative number;

Third column, do the same thing, only with (1-8x^2) instead of 4x;

Fourth column, I multiply the results from the previous two columns (e.g. positive * negative = negative);

Fifth column, I write "increasing" or "decreasing," depending on whether the fourth column says "positive" or "negative" (e.g. if the fourth column says positive, I put "increasing").

I found that on the intervals (-INF, -(sqrt(1/8))) and (-(sqrt(1/8)), 0), the function was increasing; on the intervals (0, (sqrt(1/8))) and ((sqrt(1/8)), INF), I found the function to be decreasing...

...only, that poses a problem. How could two intervals, between two zeros of f'(x), both be increasing or both be decreasing?