Find the absolute maximum and​ minimum, if either​ exists, for f(x)=x^2−14x+3. Select the correct choice below​ and, if​ necessary, fill in the answer boxes to complete your choice.

Question

Find the absolute maximum and​ minimum, if either​ exists, for f(x)=x²−14x+3.

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

A.The absolute minimum is nothing at x= ___________.

B. There is no absolute minimum.

Answer 1

SEVEN. x=7

x^2 -14x + 3

take the derivative and set equal to zero

2x -14 = 0

x = 7

(7)^2 -14(7) + 3 = 49-98+3 = -46 = local & global, absolute minimum. It's the vertex (7,-46)

x^2 -14x + 3 = 0

complete the square

x^2 -14x + 49 = -3+49 = 46

(x-7)^2 = 46

x-7 = + or - sqr46

x = 7 + or - sqr46 = about 0.2 or 13.8= x intercepts. y intercept = 3 (0,3)

axis of symmetry is x=7.

lucky 7 is where the absolute minimum is: (7,-46), there is no local or global maximum. the range is [-46,+infinity) no limit to how high you can go. It just goes forever higher & higher.