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?

Ignore the scribble, please.

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)<0` for
`x<0`, 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...