I'd say the graph's qualitative behavior is correct. Once you get to the arctic circle, there are singularities in the rate of change of the length of daylight.
For example, if you're at the North Pole, the sun is below the horizon all winter, and then on the vernal equinox rises above the horizon and does not set again until the autumnal equinox. So, formally, the rate of change in daylight is zero all year long, except on the equinoxes when it is infinite. Any latitude above the Arctic Circle will have these kinds of singularities.
In practice there are some corrections to the amount of daylight that I discuss at the bottom of the article, the most important of which is the effect of atmospheric refraction. If you were standing on the North Pole, you'd actually observe the Sun appear to rise some time before the vernal equinox.
For example, if you're at the North Pole, the sun is below the horizon all winter, and then on the vernal equinox rises above the horizon and does not set again until the autumnal equinox. So, formally, the rate of change in daylight is zero all year long, except on the equinoxes when it is infinite. Any latitude above the Arctic Circle will have these kinds of singularities.
In practice there are some corrections to the amount of daylight that I discuss at the bottom of the article, the most important of which is the effect of atmospheric refraction. If you were standing on the North Pole, you'd actually observe the Sun appear to rise some time before the vernal equinox.