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$f(x)=5x - 9$\n(a) $0,3$\n(b) $-2,4$\n(a) the absolute maximum value is 6 at $x = 3$\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$f(x)=5x - 9$\n(a) $0,3$\n(b) $-2,4$\n(a) the absolute maximum value is 6 at $x = 3$\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 derivative

The function (f(x)=5x - 9) has a derivative (f^\prime(x)=5). Since (f^\prime(x)>0) for all (x), the function is increasing on the entire real - line.

Step2: Evaluate the function at the endpoints of the interval ([0,3])

  • When (x = 0): (f(0)=5\times0-9=-9)
  • When (x = 3): (f(3)=5\times3 - 9=15 - 9 = 6)

Answer:

The absolute minimum value is (-9) at (x = 0)