If f(x) ~ f(a) + f'(a)(x - a), then:
f(x) - f(a) ~ f'(a)(x - a), and assuming x - a is sufficiently small, and f is continuous:
f'(a) ~ [f(x) - f(a)]/(x - a).
Put another way, you cannot actually find N'(t) = dN/dt, but you CAN find ΔN/Δt, where Δt = 1 year.
The graph of N will be composed of line segments (well, dots, actually, but we tend to "connect the dots").
You will actually get two slopes, one for the segment on each side of each t. It might be a good idea to average the two numbers you get for 2005,2006 and 2007 (and perhaps you see why you are not asked about 2004 and 2008).