Let's picture a graph, where the x variable is a central bank's official interest rate and the y variable is the resulting economic benefit. Let's call the graph "The H-Curve".
The line is curved, or non?linear, because the 'economic benefits' slope will differ at every point along the curve. This is somewhat obvious as a slope measures the rate of change and central bankers admit that their effectiveness weakens over time and with each successive ease.
This admission though suggests that marginally declining utility will eventually cause the slope to flatten to a point at which further accommodation will simply provide no economic benefit. However, the broader truth more likely is that central bank stimulus is actually a parabolic function, whereby the slope goes negative at a certain point. The parabola's vertex peak point signifies the optimal level of stimulus and anything further is a cost or negative benefit.