Single Variable Calculus, Chapter 4, 4.3, Section 4.3, Problem 6

Below is the graph of the derivative of the function



a.) At what intervals is $f$ increasing or decreasing?
b.) At what values of $x$ does $f$ have a local maximum or minimum?

a.) Based from the graph, the function is increasing (where $f'$ is positive) at interval $0 < x < 1 $ and $3 < x < 5$. On the other hand, the function is decreasing (where $f'$ is negative) at intervals $1 < x < 3 $ and $5 < x < 6$

b.) Since the sign of the derivative changes from negative to positive at $x= 3$ and positive to negative at $x = 1$ and $x = 5$. We see that $f(x)$ has a local maximum at $x = 5$ and local minimum at $x = 3$