Please help me solve this Physical Pendulum problem?

(a)

The weight of the stick is solely responsible for its torque.

Iθ" = mgx sinθ

Find the moment of inertia of the stick at different pivot points via the parallel axis theorem.

(mL²/12 + mx²)θ" = mgx sinθ

(L²/12 + x²)θ" = gx sinθ

For small oscillations sinθ ≈ θ.

θ" = [gx / (L²/12 + x²)] θ

ω² = gx / (L²/12 + x²)

d(ω²)/dx = [(L²/12 + x²)(g) - (gx)(2x)] / (L²/12 + x²)² = 0

g(L²/12 - x²) = 0

x = L/sqrt(12)

(b)

ω² = [gL/sqrt(12)] / (L²/12 + L²/12)

ω² = [g/sqrt(12)] / (L/6)

(2π/T)² = g sqrt(3) / L

T = 2π sqrt{L / [g sqrt(3)]}