2 Locate all extrema for the function $y=x^{2}-6 x+5$ on the interval $[0,7]$.
(Remember to include a graph of the function on the given interval; as you move forward in math we won't ask you to graph, you just do it)

Step 1 ：First, we need to find the derivative of the function \(y=x^{2}-6 x+5\). The derivative is \(f'(x) = 2x - 6\).

Step 2 ：Next, we set the derivative equal to zero to find the critical points: \(2x - 6 = 0\). Solving for \(x\), we find that the critical point is \(x = 3\).

Step 3 ：We then use the second derivative test to determine whether this point is a local minimum, maximum, or saddle point. The second derivative of the function is \(f''(x) = 2\), which is always positive, so \(x = 3\) is a local minimum.

Step 4 ：We evaluate the function at the critical point and at the endpoints of the interval to find the extrema. The function value at \(x = 3\) is \(-4\), at \(x = 0\) is \(5\), and at \(x = 7\) is \(12\).

Step 5 ：Finally, we compare these values to find the minimum and maximum values of the function on the interval \([0,7]\). The minimum value is \(-4\) at \(x = 3\) and the maximum value is \(12\) at \(x = 7\).