Question

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur

$t(x)=7x - 1,-4,3$

the absolute maximum value is 20 at $x = 3$
(use a comma to separate answers as needed)

the absolute minimum value is $\square$ at $x=\square$
(use a comma to separate answers as needed)

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 \(x=-4\)