Find the Largest Value of the Function y = 4cos (x-n / 12)

1. Since the argument of the function – (x – π / 12), can take any values, the cosine function takes values in the range [-1; one]:
cos (x – π / 12) ≥ -1; (one)
cos (x – π / 12) ≤ 1. (2)
2. Multiplying both sides of the second inequality by 4, we find the largest value of the given trigonometric function:
f (x) = 4cos (x – π / 12);
4cos (x – π / 12) ≤ 4;
f (x) ≤ 4;
fmax = 4.
Answer. The largest value of the function is 4.