The function is given as
[tex]f(x)=4\cos (\pi x)+1[/tex]For the equation of mid-line ,
From the function, we have a vertical shift up 1.
So the mid-line is y=1.
Maximum -
The amplitude of the function is 4.
From 1, you can go up 4 values to find the maximum.
Therefore, the maximum is 1+4=5
Minimum-
The amplitude of the function is 4.
From 1, you can go down 4 values to find the minimum.
Therefore, the minimum is 1-4=-3.