How do you find the intervals of increasing and decreasing using the first derivative given #y=2x+1/x#?

1 Answer
Noah G
May 27, 2017

#(-oo, -1/sqrt(2))#
#(-1/sqrt(2), 1/sqrt(2))#
#(1/sqrt(2), oo)#

Explanation:

The function can be written as

#y= 2x + x^-1#

Which differentiates to:

#y' = 2 - x^-2 = 2 - 1/x^2#

A function will change from increasing to decreasing and vice versa when the derivative equals #0#.

#0 = 2 - 1/x^2#

#1/x^2 = 2#

#1/2 = x^2#

#x =+-1/sqrt(2)#

Now select a test point, let it be #x = 1#. Evaluating within the derivative gives a positive value which means the function is increasing at that Point. It also means that the function is decreasing on #-1/sqrt(2) < x < 1/sqrt(2)#.

Hopefully this helps!

Related questions
See all questions in Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)
Impact of this question
1703 views around the world
You can reuse this answer
Creative Commons License