Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you find the critical numbers for #f(x)= x^(-8) ln x# to determine the maximum and minimum?

1 Answer

Oct 22, 2016

The function has no critical numbers.

Explanation:

A critical number for #f# is a number #c# in he domain of #f# where #f'(c) = 0# or #f'(c)# does not exist.

#f(x) = x^-8 = 1/x^8# has domain: all reals except #0#.

#f'(x) = -8x^-7# is never #0# and fails to exist only at #0#, which is not in the domain of #f#. So, #f# has no critical numbers.

Related questions

See all questions in Identifying Stationary Points (Critical Points) for a Function

Impact of this question

4003 views around the world

You can reuse this answer
Creative Commons License