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$f(x)=7x - 1,-4,3$\nthe absolute maximum value is at $x=$\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$f(x)=7x - 1,-4,3$\nthe absolute maximum value is at $x=$\n(use a comma to separate answers as needed)

Answer

Explanation:

Step1: Find the derivative of the function

The function is (f(x) = 7x - 1). The derivative (f^\prime(x)=\frac{d}{dx}(7x - 1)=7). Since (f^\prime(x)=7>0) for all (x), the function (y = f(x)) is increasing on the interval ([-4,3]).

Step2: Evaluate the function at the endpoints of the interval

  • When (x=-4), (f(-4)=7\times(-4)-1=-28 - 1=-29).
  • When (x = 3), (f(3)=7\times3-1=21 - 1=20).

Answer:

The absolute maximum value is (20) at (x = 3)