Final answer:
The maximum and minimum values of the function f(x) = 5/(4+3*cos(2x)) can be found through direct calculation by evaluating the function 4+3*cos(2x), using calculus to find critical points, or employing numerical methods. All choices (A, B, and C) are valid approaches.
Step-by-step explanation:
To find the maximum and minimum values of the cosine function f(x) = \frac{5}{4+3\cos(2x)}, option (A) involves finding the maximum and minimum of 4+3\cos(2x) and then dividing by 5. Because cosine oscillates between -1 and +1, the maximum of 4+3\cos(2x) will be 7 when cos(2x) equals 1, and the minimum will be 1 when cos(2x) equals -1. Thus, for f(x), the maximum value occurs when cos(2x) is at its minimum (-1), and the minimum value of f(x) occurs when cos(2x) is at its maximum (1).
Using calculus (option B), we could find the critical points by taking the derivative of f(x) and setting it to zero, then determining which are maxima or minima. This approach requires understanding of derivative rules and how they apply to trigonometric functions.
Alternatively, option (C) suggests the use of numerical methods to approximate the maxima and minima of the function. This approach is practical when the function is complex or when an analytic solution is difficult to obtain. Numerical methods can involve algorithms such as the Newton-Raphson method or software applications that provide numerical approximations.
Therefore, the answer is (D) All of the above, since each of these methods can be used to determine the maximum and minimum values of the given function.