f(x) = 3 cos 5 x, minimum value of the function f(x)
The general form of a cosine function is given by f(x) = A cos(B(x - C)) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
Comparing this to the given function f(x) = 3 cos 5x, we can see that A = 3, B = 5, C = 0, and D = 0.
The minimum value of the function occurs when the cosine function is equal to its minimum value, which is -1. This occurs when the argument of the cosine function is π radians out of phase (or one half of a period) from the usual cosine function (i.e., when B(x - C) = π/2).
So, setting B(x - C) = π/2, we have 5x = π/2.
Solving for x, we get:
x = π/10.
So, the minimum value of the function f(x) = 3 cos 5x is f(π/10) = 3 cos (5 * π/10) = 3 cos (π/2) = 3 * (-1) = -3.