602. Find the greatest and the least values of the function $y=$ $=x^{5}-5 x^{4}+5 x^{3}+3$ on the interval $[-1,2]$.
Solution. $1^{0}$. Find the critical points belonging to the interval $(-1,2)$, and the values of the function at these points:

$$
\begin{gathered}
y^{\prime}=5 x^{4}-20 x^{3}+15 x^{2} ; 5 x^{4}-20 x^{3}+15 x^{2}=0 ; 5 x^{2}\left(x^{2}-4 x+3\right)=0 \\
x_{1}=0, x_{2}=1, x_{3}=3
\end{gathered}
$$

The critical point $x_{3}=3$ does not belong to the given interval.

We calculate the values of the function at the other two critical points: $y(0)=3, y(1)=4$.

$2^{0}$. We calculate the values of the function at the endpoints of the given interval: $y(-1)=-8 ; y(2)=-5$. The value of the function $y(1)=4$, the smallest value is $y(-1)=-8$.