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)=6x - 4;-5,3

the absolute maximum value is at x=
(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: Find the derivative of the function

The derivative of \( f(x)=6x - 4\) is \( f^\prime(x)=6\). Since \( f^\prime(x)=6>0\), the function is increasing on the interval \([-5,3]\).

Step2: Evaluate the function at the endpoints

• For \(x=-5\): \(f(-5)=6\times(-5)-4=-30 - 4=-34\)
• For \(x = 3\): \(f(3)=6\times3-4=18 - 4 = 14\)

Answer:

The absolute maximum value is \(14\) at \(x = 3\).
The absolute minimum value is \(-34\) at \(x=-5\).