f(x) = 3 cos 5 x, x belongs to R , find the minimum value of the function f(x)

Answer 1

The function f(x) = 3 cos 5x is a periodic function with a period of 2π/5.

To find the minimum value of the function, we need to find the x-value at which the cosine function reaches its minimum value of -1.

Since the cosine function has a maximum value of 1, we know that it will reach its minimum value when the argument of the cosine function, 5x, is equal to (2n + 1)π, where n is any integer.

Solving for x in this equation, we have:
5x = (2n + 1)π
x = (2n + 1)π/5

Therefore, the minimum value of the function f(x) occurs at x = (2n + 1)π/5, where n is any integer.