find the absolute maximum and minimum values of the following function on the given interval. then graph the…

find the absolute maximum and minimum values of the following function on the given interval. then graph the function.\nf(x)=\frac{7}{9}x - 4, - 4leq xleq3\n\nfind the absolute maximum value. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.\n\na. the absolute maximum value occurs at x = \n(simplify your answers. use a comma to separate answers as needed.)\nb. there is no absolute maximum.

find the absolute maximum and minimum values of the following function on the given interval. then graph the function.\nf(x)=\frac{7}{9}x - 4, - 4leq xleq3\n\nfind the absolute maximum value. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.\n\na. the absolute maximum value occurs at x = \n(simplify your answers. use a comma to separate answers as needed.)\nb. there is no absolute maximum.

Answer

Explanation:

Step1: Identify the function type

The function $f(x)=\frac{7}{9}x - 4$ is a linear function. The slope $m=\frac{7}{9}>0$, so the function is increasing.

Step2: Evaluate the function at endpoints

Evaluate $f(x)$ at $x=-4$ and $x = 3$. For $x=-4$, $f(-4)=\frac{7}{9}\times(-4)-4=-\frac{28}{9}-4=-\frac{28 + 36}{9}=-\frac{64}{9}$. For $x = 3$, $f(3)=\frac{7}{9}\times3-4=\frac{7}{3}-4=\frac{7 - 12}{3}=-\frac{5}{3}$. Since the function is increasing on the interval $[-4,3]$, the maximum value occurs at the right - hand endpoint.

Answer:

A. The absolute maximum value $-\frac{5}{3}$ occurs at $x = 3$.