Question

I don't see how a 4 digit code can be formed given that the antiderivative is a cubic. Can anyone give me insight?

Answer 1

I believe what this question is saying (albeit poorly) is that you have 4 possible ways to encode what happens on a given interval between critical points, and not that the sequence you would submit as an answer consists of 4 digits.

For a basic example, let's consider $f(x)=x^3$. We have

$f'(x)=3x^2$

so that $x=0$ is the only critical point, and

$f''(x)=6x$

so that $x=0$ is the only inflection point.

$f'(x)>0$ for all $x$, while $f''(x)$ for $x$, and vice versa.

We have two intervals to work with, $(-\infty,0)$ and $(0,\infty)$. So in this case, the answer would be 2 over $(-\infty,0)$ and 1 over $(0,\infty)$.

That's a guess at any rate. Also, I don't know how helpful this is 4 days after the fact...