Question

Hi there, I am having some trouble solving the following question relating to where a function is increasing and decreasing.

Answer 1

From the graph, we can identify critical points. At these points, there is a change between increasing and decreasing behavior.

These points are:

$\begin{gathered} x=0\text{ \lparen from decreasing to increasing\rparen} \\ x=3\text{ \lparen from increasing to decreasing\rparen} \end{gathered}$

Additionally, there is a discontinuity at x = 4, but the function is still decreasing for x > 4.

Finally, we conclude that:

f(x) is increasing for x in:

$(0,3)$

f(x) in decreasing for x in:

$(-\infty,0)\cup(3,4)\cup(4,+\infty)$