Show that any cubic f(x)=a x^3+b x^2+c x+d has one inflection point. Find conditions on the coe…

Show that any cubic f(x)=a x^3+b x^2+c x+d has one inflection point. Find conditions on the coefficients a-e that guarantee that the quartic f(x)=a x^4+b x^3+c x^2+d x+e has two inflection points.

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derivative function 3: calculating rates of change, intervals of concavity and inflection points
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