Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do use the first derivative test to determine the local extrema #f(x) = x / (x^2+1)#?

1 Answer

Sep 29, 2015

See the explanation.

Explanation:

#f'(x)=(x^2+1-2x^2)/(x^2+1)^2=(1-x^2)/(x^2+1)^2#

#f'(x)=0 <=> 1-x^2=0 <=> x=1 vv x=-1#

#f'(x)>0# #AAx in (-1,1)# function increasing
#f'(x)<0# #AAx in (-oo,-1)uu(1,oo)# function decreasing

#f'(x)# changes sign at #x=-1# and #f(x)# has a minimum value #f_min=f(-1)=-1/2#

#f'(x)# changes sign at #x=1# and #f(x)# has a maximum value #f_max=f(1)=1/2#

Related questions

See all questions in Identifying Turning Points (Local Extrema) for a Function

Impact of this question

1242 views around the world

You can reuse this answer
Creative Commons License