The function is f(x) = 2x⁴ - 4x² + 6.

If f^,(x) > 0 (Positive) for all x in (a, b), then f(x) is increasing on [a, b].

If f^,(x) < 0 (Negative) for all x in (a, b), then f(x) is decreasing on [a, b].

f^,(x) = 8x³ - 8x = 8x(x² - 1) = 0.

The key numbers are x = 0 and x = ± 1.

Test intervals    x - Value                Polynomial value                              Conclusion

(- ∞, - 1)            x = - 2            8(- 2)³ - 8(- 2) = - 64 + 16 = - 48 < 0        Decreasing

(- 1, 0)               x = - 0.5         8(- 0.5)³ - 8(- 0.5) = - 1 + 4 = 3 > 0         Increasing

(0, 1)                 x = 0.5           8(0.5)³ - 8(0.5) = 1 - 4 = - 3 < 0              Decreasing

(1, ∞)                x = 2              8(2)³ - 8(2) = 64 - 16 = 48 > 0                Increasing

So, f(x) is increasing on the interval (- 1, 0) and (1, ∞) and decreasing on the interval (- ∞, - 1) and (0, 1).