To find points of inflection you solve and test the nature of the solution.
To justify the existence of a point of inflection at you need to show that has a turning at .
Note that (why?)
If has a turning point then N = N(t) has a point of inflection. The point of inflection occurs at the value of N corresponding to the N-coordinate of the turning point of .
Since is a quadratic function it's not difficult to:
1. establish that has a turning point.
2. find the N-coordinate of the turning point.