Answer
(a) see the graph below, there are 2 local extrema;
(b) see the prove below.
Work Step by Step
(a) We graph the function as shown in the figure. Clearly we can see that there are 2 local extrema:
one maximum between 2 and 4, and one minimum between 4 and 5.
(b) Since $a,b,c$ are three zeros of the function and $a\lt b\lt c$, we can imagine there are three points
on the $x$-axis labeled $a,b,c$ from left to right (for example, 2,4,5 in the figure). Since the given 3rd degree
polynomial is a smooth and continuous function passing through these zero locations, there must be one extreme point between each adjacent two zeros because the curve passing the first zero must return and pass the second. As there are three zero locations on the $x$-axis, we conclude that this function must have two local extrema.
