Question

Suppose that the differential equation dx/dt = f(x) has a stationary point x* where f'(x*) < 0. We saw that the point x* is a stable fixed point for x{n}+1 = x{n} + hf(x{n}), provided that h < 2/|f'(x*)|. Assuming that x{0} is sufficiently close to x*, show that if h > 1/|f'(x*)| then x{n} is alternately greater than and less than x*, while if h < 1/|f'(x*)| the orbit x{n} approaches x* monotonically.
WTF. ({...} = subscript)