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f(x) graph based on derivative graph help

Hello MHF,

I am stuck on part c of this question and am not 100% sure on a and b either. There is a table involved. It is attached.

Attachment 9426

a) What are the x-coordinates of all absolute maximum and absolute minimum points of $\displaystyle f$ on the interval $\displaystyle \left[-3, 3\right]$. Justify your answer.

b)What are the x-coordinates of all points of inflection of $\displaystyle f$ on the interval $\displaystyle \left[-3, 3\right]$? Justify your answer.

c) Sketch a graph that satisfies the given properties of $\displaystyle f$.

a-answer) i got $\displaystyle x=1$ for a maximum because the $\displaystyle f'(x)$ goes from negative y values to 0 back to negative y values. is this correct?

b-answer) point of inflections occurs when $\displaystyle f''(x)=0$ and thats and $\displaystyle x=1$, I don't think there are any other points, correct?

c-answer) i could never figure out how to do that on MHF but i have seen other people do it. All my graphs don't seem to work, but from the chart i think there are 2 separate functions?

any help, especially with c would be greatly appreciated. Thanks.