Question

Let f(x) = x⁻⁷ in (x) . (a) find the relative maximum and relative minimum values, if any, of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.) relative maximum values: relative minimum values:dne complete the following parts.

(1) the domain of the function fis (0,infinity ) (enter your answer using interval notation.)
(2) to determine the relative maximum and relative minimum values of the function f we need the critical numbers of f

Answer 1

The function f(x) = x^-7 does not have any relative maximum or minimum values.

Step-by-step explanation:

The function f(x) = x-7 is continuous for all values of x except 0, since division by 0 is undefined. Hence, the domain of the function is (0, infinity). However, since the function is a power function with a negative exponent, it approaches infinity as x approaches 0. Therefore, there is no relative maximum or relative minimum value for the function. In other words, there are no relative maximum or relative minimum values for the function.