Determine from the graph whether f possesses extrema on the interval (a,b).
Maximum is at the x=c, and minimum at x=b???
Unfortunately, there is no way to answer the question based on the drawing; if the graph were of a better quality then maybe.
For example, in we know absolutely that $\displaystyle \lim _{x \to c^ - } f(x) \le f(c)$ then you could say that $\displaystyle x=c$ is a extreme maximum. But that is not clear from your drawing.
The second problem with the question is that the notation $\displaystyle (a,b)$ is a open interval. Thus, there would be no minimum at $\displaystyle x=b$ because $\displaystyle b$ is not in the domain of interest. If however it were $\displaystyle [a,b]$, a closed interval, the $\displaystyle x=b$ would be the absolute minimum,