First, find the critical points by setting \(f'(x) = 0\):

\(x^3 + 2x^2 - 4x + 7 = 0\).

Differentiate \(f'(x)\) to find \(f''(x)\):

\(f''(x) = 3x^2 + 4x - 4\).

Find the roots of \(f''(x)\) to determine intervals of increase/decrease:

\(3x^2 + 4x - 4 = 0\).

Using the quadratic formula, \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), we find:

\(x = \frac{-4 \pm \sqrt{16 + 48}}{6} = \frac{-4 \pm 8}{6}\).

This gives \(x = \frac{2}{3}\) and \(x = -2\).

Test intervals around these points:

For \(-2 < x < \frac{2}{3}\), \(f'(x) < 0\).

For \(x > \frac{2}{3}\), \(f'(x) > 0\).

Since \(f'(x)\) changes sign, \(f\) is neither increasing nor decreasing.