Question

2x-x^3>=0

solve for x

Answer 1

2x-x^3 >= 0

x(2-x^2) >= 0

This function crosses the x-axis at the roots, which are at

x = -√2, 0, √2

Now, you know that y is negative for large negative x, so

y < 0 in (-∞,-√2)
y >= 0 in [-√2,0]
y < 0 in (0,√2)
y >= 0 in [√2,∞)