Given
[tex]y=x^2-6x+8[/tex]To obtain the minimum value of y, we first take the derivative of y
The derivative of y is:
[tex]y^{\prime}=2x-6[/tex]Equating
[tex]y^{\prime}\text{ = 0}[/tex]gives the minimum value we require.
Doing that, we have:
[tex]2x-6=0[/tex]So that
[tex]\begin{gathered} 2x=6 \\ x=\frac{6}{2} \\ =3 \end{gathered}[/tex]Therefore, the minimum value is x = 3
