Message #193327

[Kaulus7]

I could probably do this myself but my mind is addled and I need to go to bed early so...

For what values of c does the polynomial P(x)=x⁴+cx³+x² have two inflection points? One inflection point? None? Illustrate by graphing P for several values of c. How does the graph change as c decreases?

I know that second derivative is the first step (I hope it is...). But how would I go about to determining the values of c? Guess and check is an option, but I don't think that's what my instructors had in mind...