IB Mathematics Analysis and Approaches Question Type 6: Finding the Regions of the Function in Which It Is Concave Up and Concave Down with Technology Exercises

Determine where $f(x)=\frac{x}{x^2+1}$ is concave up and concave down.

Find where the function $f(x)=\frac{1}{1+x^2}$ is concave up and concave down.

Determine the concavity regions for $f(x)=x{e}^{-x}$.

Using technology, determine the concavity of $f(x)=\sin x+x^2$ on its domain.

Find the intervals of concavity for $f(x)=x^4-4x^3+4x$.

Find the regions where the function $f(x)=x^3-6x^2+9x+2$ is concave up and concave down.

Consider the function $f(x)=e^{-x^2}$.

Using calculus, determine the intervals where the graph of $f$ is concave up and concave down. Give your answers in exact form.

Using a graphing tool, find the intervals of concavity for $f(x)=\ln (e^{2x}+2x)$.

Find the intervals on which the graph of $f(x)=\frac{e^x}{1+e^x}$ is concave up and concave down.

Determine the intervals of concavity for $f(x)=x^5-5x$.

Find the intervals of concavity for $f(x)=\ln (x^2+1)$.