How do you find the critical numbers for #cos (x/(x^2+1))# to determine the maximum and minimum?

1 Answer
Jul 30, 2016

Answer:

So the critical point is #x=0#

Explanation:

#y= cos(x/(x+1))#
Critical point : It is the point where the first derivative zero or it does not exist.
First find the derivative , set it to 0 solve for x.
And we need to check is there a value of x which makes the first derivative undefined.

#dy/dx=-sin(x/(x+1)). d/dx(x/(x+1))#( use chain rule of differentiation)

#dy/dx=-sin(x/(x+1))((1(x+1)-x.1)/(x+1)^2)#Use product rule of differentiation.

#dy/dx=-sin(x/(x+1))((1)/(x+1)^2)#

Set dy/dx=0
#-sin(x/(x+1))/(x+1)^2=0#
#rArrsin(x/(x+1))/((x+1)^2)=0#
#sin(x/(x+1))=0 rArr x/(x+1)=0 rArr ,x=0#

So the critical point is #x=0#