Answer
$(a)$ Local minimum or local maximum points stand for the maximum or minimum value that the graph of a function takes in a specific viewing rectangle.
$(b)$ A graph of a function $P$, of a degree $n$ can have at most $(n-1)$ local extrema.
Work Step by Step
$(a)$ Local minimum or local maximum points stand for the maximum or minimum value that the graph of a function takes in a specific viewing rectangle.
The point $(x, P(x))$ is local maximum (or minimum) point of a function, if it is the highest (or lowest) point of the graph of $P$ within specific viewing rectangle.
$(b)$ In general, a graph of a function $P$, of a degree $n$ can have at most $(n-1)$ local extrema.