Question

Find the critical numbers of the function g(x)=8−2tan(x). (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.)

A. nπ, where n is an integer
B. 2(2n+1) 2π , where n is an integer
C. 2n 2π , where n is an odd integer
D. 2n 2π , where n is an even integer

Answer 1

To find the critical numbers of the function g(x)=8−2tan(x), we need to determine the values of x where the derivative is equal to zero or does not exist. This will give us the x-values where the function may have local extrema or points of inflection. However, in this case, there are no critical numbers for the function.

Step-by-step explanation:

To find the critical numbers of the function g(x)=8−2tan(x), we need to determine the values of x where the derivative is equal to zero or does not exist. This will give us the x-values where the function may have local extrema or points of inflection.

First, we find the derivative of g(x). The derivative of tan(x) is sec^2(x), so the derivative of g(x) is -2sec^2(x). Setting this equal to zero, we get:

-2sec^2(x) = 0

Since the secant function is never equal to zero, there are no critical numbers for this function. Therefore, the answer is DNE (Does Not Exist).