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

Find any inflection points of $f(x)=x^5-5x$.

Find the coordinates of the points of inflection on the graph of $f(x)=3x^4-8x^3+6x^2$.

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

Determine the inflection point of the function $f(x) = 5x^3 + 6x^2 + x + 2$.

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

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

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

Does the function $f(x)=x^4-4x^3+6x^2$ have any inflection point? If so, find it.

Does $f(x)=\ln(x)$ have an inflection point on its domain? If so, find it.