Solution below.

Reveal solution by highlighting:

With this one, I had to noodle around for a while, before I hit the solution.

Let g(x) = -x³+2x²+6x-9 and h(x) = x²-2x+3. Further, f(x) = ax+b. Then g(x) <= f(x) <= h(x). We know this has to be true for 0 <= x <= 3, at every possible value of x. Just for fun, let’s look at a picture from wolframalpha.

Some further investigations shows, g(2) = h(2) = 3. Even more fun, g'(2) = h'(2) = 2. If f(x) is going to fit between g and h:

f(2) = 3 and f'(2) = 2

<=> a2+b = 3 and a = 2

<=> 2*2+b = 3 and a = 2

<=> b = 3-2*2 = -1 and a = 2.

So f(x) = 2x-1. Therefore f(200) = 2*200-1 = 399.