Answer
Increasing on $(1,5)$ and decreasing on $(0,1) U (5,6)$
Local maximum at $x=5$ and local minimum at $x=1$
Work Step by Step
Refer to the graph, which is a graph of $f'(x)$
When the derivative is positive, $f(x)$ is increasing. $f'(x)$ is positive on $(1,5)$
When the derivative is negative, $f(x)$ is decreasing. $f'(x)$ is negative on $(0,1) U (5,6)$
Local maxima occur when the derivative goes from positive to negative (crosses the x axis from top to bottom). This occurs at $x=5$
Local minima occur when the derivative goes from negative to positive (crosses the x axis from bottom to top). This occurs at $x=1$
