find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x…

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur.\n$f(x)=6x + 7$\n(a) $0,9$(b) $-2,6$\n(a) the absolute maximum value is 61 at $x = 9$\n(use a comma to separate answers as needed.)\nthe absolute minimum value is $\\square$ at $x=\\square$\n(use a comma to separate answers as needed.)

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur.\n$f(x)=6x + 7$\n(a) $0,9$(b) $-2,6$\n(a) the absolute maximum value is 61 at $x = 9$\n(use a comma to separate answers as needed.)\nthe absolute minimum value is $\\square$ at $x=\\square$\n(use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Analyze the function's monotonicity

The function (f(x) = 6x + 7) is a linear function with a slope (m = 6>0). A linear function (y=mx + b) ((m>0)) is increasing on the entire real - line.

Step2: Evaluate the function at the endpoints of the interval ([0,9])

For the left - hand endpoint (x = 0): (f(0)=6\times0 + 7=7) For the right - hand endpoint (x = 9): (f(9)=6\times9+7=54 + 7=61)

Since the function is increasing, the minimum value occurs at the left - hand endpoint of the interval and the maximum value occurs at the right - hand endpoint of the interval.

Answer:

The absolute minimum value is (7) at (x = 0)