F' (x) = 2xe (-x 4) Let F'(x)=0, when x=0.

∴ The monotonic increasing interval of f(x) is: (0, +∞), and the monotonic decreasing interval of f (x) is: (-∞, 0).

f''(x)=2e^(-x^4)-8x^4e^(-x^4)=2( 1-4x^4)e^(-x^4)

Let F''(x)=0 x = √ 2/2 when x

The convex interval of ∴F(x) is: (-∞, -√2/2), (√2/2,+∞); The concave interval of F(x) is: (-√2/2, √2/2).