Question
Show that every polynomial function of degree 3 $f(x)=a x^{3}+b x^{2}+c x+d$ has exactly one inflection point.
Step 1
An inflection point occurs where the second derivative of the function changes sign, which typically happens where the second derivative is zero. Show more…
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Show that the general quartic (fourth-degree) polynomial $f(x)=x^{4}+a x^{3}+b x^{2}+c x+d$ has either zero or two inflection points, and the latter case occurs provided that $b<3 a^{2} / 8$.
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