how to get the maximum value of function f:f(X) = 2 sin4X
To find the maximum value of the function f(X) = 2sin^4(X), we need to understand the behavior of the sine function and its range.
1. The maximum value of the sine function is 1.
2. The sine function oscillates between -1 and 1.
3. The function f(X) = 2sin^4(X) will always be positive, as the fourth power ensures a positive result.
To find the maximum value of f(X) = 2sin^4(X), we need to determine when the sine function has a maximum value of 1. This occurs when the input angle of the sine function is π/2.
Therefore, to maximize f(X), we set X = π/2, and the maximum value of f(X) will be 2sin^4(π/2) = 2(1)^4 = 2.
So, the maximum value of the function f(X) = 2sin^4(X) is 2.