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

1 Answer
Jothi S.
Jul 30, 2016

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

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