Find the minimum and maximum values of the function $y=3 x^{2}-6 x+5$ on the interval $[0,6]$ by comparing values at the critical points and endpoints.
(Use symbolic notation and fractions where needed. If the function does not have extreme values, enter DNE.)
\[
y_{\min }=
\]
\[
y_{\max }=
\]

Step 1 ：Find the derivative of the function \(y=3x^2-6x+5\), which is \(y'=6x-6\).

Step 2 ：Set the derivative equal to zero to find the critical points: \(6x-6=0\).

Step 3 ：Solve for x to get the critical point: \(x=1\).

Step 4 ：Evaluate the function at the critical point and at the endpoints of the interval [0,6]: \(y(0)=5\), \(y(1)=2\), and \(y(6)=89\).

Step 5 ：The minimum value of the function on the interval [0,6] is 2 and the maximum value is 89.

Step 6 ：Check that these results meet the requirements of the problem. The minimum and maximum values are indeed on the interval [0,6], and the function is defined and continuous on this interval.

Step 7 ：Therefore, the minimum value of the function is \(\boxed{2}\) and the maximum value of the function is \(\boxed{89}\).