Question Type 7: Finding the regions of concavity without technology Exercises

Determine the regions of concavity and inflection points for $f(x)=\sqrt{x^2+4}\,$.

Determine the regions where the function $f(x)=x^3$ is concave up and concave down, and identify any inflection points.

Find the intervals of concavity and the inflection points of the graph of $f(x) = \sin x$ on the domain $[0, 2\pi]$.

Determine the regions of concavity of $f(x)=e^x$ and state whether it has any inflection points. [4 marks]

Determine the intervals of concavity and the coordinates of the points of inflection for the function $f(x)=x e^x$. [6]

Find the concavity intervals and inflection point(s) for $f(x)=\arctan x$.

Find the intervals of concavity and the coordinates of the points of inflection for the function $f(x)=e^{-x^2}$.

Find the intervals of concavity and inflection points for $f(x)=\ln\bigl(e^x+1\bigr)$ without using technology.