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.\n$f(x)=\\frac{1}{7}x + 4$, $-1\\leq x\\leq1$\nfind the absolute maximum value. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice\na. the absolute maximum value $\\square$ occurs at $x = \\square$.\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.\n$f(x)=\\frac{1}{7}x + 4$, $-1\\leq x\\leq1$\nfind the absolute maximum value. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice\na. the absolute maximum value $\\square$ occurs at $x = \\square$.\n(simplify your answers. use a comma to separate answers as needed.)\nb. there is no absolute maximum.

Answer

Explanation:

Step1: Find the derivative of the function

The derivative of (f(x)=\frac{1}{7}x + 4) is (f^\prime(x)=\frac{1}{7}). Since (f^\prime(x)=\frac{1}{7}>0), the function is increasing on the interval ([-1,1]).

Step2: Evaluate the function at the endpoints

Evaluate (f(x)) at (x=-1) and (x = 1). When (x=-1), (f(-1)=\frac{1}{7}\times(-1)+4=4-\frac{1}{7}=\frac{28 - 1}{7}=\frac{27}{7}). When (x = 1), (f(1)=\frac{1}{7}\times1+4=4+\frac{1}{7}=\frac{28+1}{7}=\frac{29}{7}).

Answer:

A. The absolute maximum value (\frac{29}{7}) occurs at (x = 1).