Question Type 5: Classifying whether specific functions have points of inflexions or not by checking the conditions on which they occur Bootcamps

Determine the inflection point(s) of $f(x)=\arctan(x)$ on $\mathbb R$.

Determine whether $f(x)=3x^4-8x^3+6x^2$ has any inflection points, and find them.

Determine the inflection points of $f(x)=\frac{1}{1+x^2}$.

Find the inflection point(s) of $f(x)=e^x x^2$.

Find the inflection point of $f(x)=x^3e^{-x}$.