Consider the function f(x)=2x+6x^(-1). For this function, there are three numbers A<B<C which are either critical or not in the domain of the function.

A=
B=
C=

f undefined for x=0

f' = 2-6/x^2
f'=0 when x=±√3

I'll let you sort them out.

To find the three numbers A, B, and C that are either critical or not in the domain of the function, we need to consider the domain of the function and any critical points where the function is undefined.

First, let's determine the domain of the function f(x) = 2x + 6x^(-1).

The function f(x) is defined for all real numbers except where the denominator (6x^(-1)) equals zero. Since x^(-1) denotes the reciprocal of x, we need to find where x = 0.

Setting the denominator equal to zero: 6x^(-1) = 0

Taking the reciprocal of both sides: x^(-1) = 0/(6*1) = 0

Since x^(-1) is equal to zero, there are no critical points or points not in the domain within the real number system.

Therefore, there are no numbers A, B, or C that are either critical or not in the domain of the function. The function is defined for all real numbers.