Question

Determine the interview on which the function is concave upward and concave downward

Answer 1

We have to identify the intervals where the function is concave upwards and where is concave downward.

We can differentiate them in a graph as:

We then have only one interval where the function is concave upwards: between x = -1 and x = 4. We can identify other intervals where the function is concave downwards and interrupted by discontinuities.

Then, we can write all the intervals as:

$\begin{gathered} (-\infty,-5)\longrightarrow\text{Concave downward.} \\ (-5,-1)\longrightarrow\text{Concave downward.} \\ (-1,4)\longrightarrow\text{Concave upward}. \\ (4,\infty)\longrightarrow\text{Concave downward.} \end{gathered}$