Question Type 6: Finding the regions of the function in which it is concave up and concave down with technology Exercises

Determine where $f(x)=\dfrac{x}{x^2+1}$ 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 $f(x)=\ln\bigl(e^{2x}+2x\bigr)$.

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

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

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