Identify the maximum and minimum values of the function y = 10 cos x in the interval [-2π, 2π].
Answer if only know
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]
The maximum value of the function (y = 10 cos x ) in the interval [-2\(\pi\),2\(\pi\)] is 10 and the minimum value of the function (y = 10 cos x ) in the interval [-2\(\pi\),2\(\pi\)] is -10.
Given :
The following steps can be used in order to determine the maximum and minimum values of the function (y = 10 cos x) in the interval [-2π, 2π]:
Step 1 - Remember the maximum value of the graph of the function (y = cos x) in the interval [-2\(\pi\),2\(\pi\)] is 1 and the minimum value of the graph of the function (y = cos x) in the interval [-2\(\pi\),2\(\pi\)] is -1.
Step 2 - From the above step, it can be said that the maximum value of the function (y = 10 cos x) in the interval [-2\(\pi\),2\(\pi\)] is 10.
Step 3 - Also from step 1, it can be said that the minimum value of the function (y = 10 cos x) in the interval [-2\(\pi\),2\(\pi\)] is -10.
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