How do you draw info about f(x) from these values of f'(x) in this ap calc question?

Question

anonymous · Answer

attachment

jhannybean · Answer

The derivative, $f'(x)$ always tells you how your main function, $f(x)$ is changing.

anonymous · Answer

mhm, so should I actually sketch f(x) in order to solve this question?

jhannybean · Answer

I'd think so, yes. The derivative is also measured as the slope of your function at the point x=....

anonymous · Answer

also, even though f'(x) tells me about the slope, I can't info for why c,d, and e are true/not true?

anonymous · Answer

@wio

amistre64 · Answer

f' doesnt define inflection points, at least not on a discrete format

amistre64 · Answer

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amistre64 · Answer

we cant even be sure of what f'(x) even looks like except at those discrete points.  so it may not even define an increasing function

jhannybean · Answer

True enough

amistre64 · Answer

inflection ... inflection .... what can f' say about inflection?

amistre64 · Answer

smoothest case has the least number of inflections
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i agree with the inflection stuff