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\n$t(x)=7x - 1,-4,3$\n\nthe absolute maximum value is 20 at $x = 3$\n(use a comma to separate answers as needed)\n\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\n$t(x)=7x - 1,-4,3$\n\nthe absolute maximum value is 20 at $x = 3$\n(use a comma to separate answers as needed)\n\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 (t(x) = 7x - 1) is a linear function. The slope (m = 7>0), so the function is increasing on the interval ([-4,3]).

Step2: Calculate the function values at the endpoints

  • When (x=-4): (t(-4)=7\times(-4)-1=-28 - 1=-29)
  • When (x = 3): (t(3)=7\times3-1=21 - 1 = 20)

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 (-29) at (x=-4)