Find the minimum and maximum values of the function $y=3x^2-6x+5$ 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 $y^{\prime }=6x-6$.

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 $\boxed{{\displaystyle 2}}$ and the maximum value of the function is $\boxed{{\displaystyle 89}}$.