The function f(x) = x^4 - 2x^2 is increasing on

The correct answer is Option (1) → \((-1, 0) \cup (1, \infty)\)

f is increasing where \(f'(x) \gt 0\).

    \(f'(x) = 4x^3 - 4x = 4x(x + 1)(x - 1)\)

The critical points \(x = -1, 0, 1\) split the line into four intervals. The sign of \(f'(x)\) on each:

    \(x \lt -1\): \((-)(-)(-)\), negative
\(-1 \lt x \lt 0\): \((-)(+)(-)\), positive
\(0 \lt x \lt 1\): \((+)(+)(-)\), negative
\(x \gt 1\): \((+)(+)(+)\), positive

So f is increasing on \((-1, 0) \cup (1, \infty)\).