11.5.35 Find the absolute minimum value on​ [0, ∞​) for f(x)=x^2−6x+8. Select the correct choice below​ and, if​ necessary, fill in the answer boxes to complete your choice.

Question

Find the absolute minimum value on​ [0, ∞​) for f(x)=x^2−6x+8.

Select the correct choice below​ and, if​ necessary, fill in the answer boxes to complete your choice.

A.

The absolute minimum is ________ at x= _______.

B.

There is no absolute minimum.

Answer 1

x^2 -6x + 8

take the derivative and set it = 0

2x -6 = 0

2x = 6

x =6/2 =3

3^2 -6(3) + 8 = 9-18+8 = -1 = minimum

absolute & local minimum is (3,-1)

at x=3, the global&local minimum is -1