Determine the minimum and maximum value of the following trigonometric function.

Question

f, of, x, equals, minus, 5, cosine, 4, x
f(x)=−5cos4x

Answer 1

To determine the minimum and maximum values of the function \( f(x) = -5 \cos(4x) \), we first need to analyze the behavior of the cosine function.

The cosine function, \( \cos(4x) \), oscillates between -1 and 1. Therefore, we can find the maximum and minimum values of \( f(x) \) by substituting these values into the function.

1. Maximum Value:

   • When \( \cos(4x) = -1 \): \[ f(x) = -5 \times (-1) = 5 \]

2. Minimum Value:

   • When \( \cos(4x) = 1 \): \[ f(x) = -5 \times 1 = -5 \]

Thus, the maximum value of the function \( f(x) = -5 \cos(4x) \) is 5, and the minimum value is -5.

In summary:

• Maximum value: \( 5 \)
• Minimum value: \( -5 \)