Question

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur.
f(x)=5x - 9
(a)0,3 (b)-2,4
(a) the absolute maximum value is 6 at x = 3.
(use a comma to separate answers as needed.)
the absolute minimum value is - 9 at x = 0.
(use a comma to separate answers as needed.)
(b) the absolute maximum value is 11 at x = 4
(use a comma to separate answers as needed.)
the absolute minimum value is at x=
(use a comma to separate answers as needed.)

Explanation:

Step1: Analyze the function's monotonicity

The function \(f(x) = 5x - 9\) is a linear function with a slope \(m = 5>0\), so it is increasing on \((-\infty,\infty)\).

Step2: Evaluate the function at the endpoints of the interval \([-2,4]\)

For \(x=-2\):
\(f(-2)=5\times(-2)-9=-10 - 9=-19\)
For \(x = 4\):
\(f(4)=5\times4-9=20 - 9 = 11\)

Answer:

The absolute minimum value is \(-19\) at \(x=-2\)