Question

Identify the maximum and minimum values of the function y = 10 cos x in the interval [-2π, 2π].

Answer 1

We can do this by taking the derivitive to find the max and min points
y'=-10sinx
find where it equals 0 in the interval
it equals 0 at -2pi, -pi,0,pi,2pi
those are the critical points
sign chart
find the signs of the derivitive between them (see attachment)

the maximums are where the sign changes from positive to negative,
minimums are where the sign changes from negative to positive

we see we have maximums at -2pi, 0, and 2pi
minimums at -pi and pi

if we evaluate the original function at those values we get

10cos(-2pi)=10
10cos(0)=10
10cos(2pi)=10
10cos(-pi)=-10
10cos(pi)=-10

the max value of the function is 10 at x=-2pi,0, and 2pi
the min value of the function is 10 at x=-pi and pi

Answer 2

We know that the maximum and minimum values of the function y = cos x in the interval [-2π, 2π] are 1 and -1 respectively.
 
The graph of y = 8 cos x is vertical stretch by a factor of 8 units. Therefore the graph y=cos x, = the maximum and minimum values of the function y = cos x in the interval [-2π, 2π]. So they are 8 and -8 respectively.  

max = 8,  ∈[−2π,2π]
                                                    = Solution 
min = −8.  ∈[−2π,2π]