What is the critical f(x)=ln(2+sin(x)) ?

The critical f(x)=ln(2+sin(x)) is x= pi/2+2pin,x=(3pi)/2+2pin

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critical f(x)=ln(2+sin(x))

critical points

f (x) = ln (2 + sin (x))

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

ln (2 + sin (x))

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Identify critical points not in

f (x)

domain

Domain of

ln (2 + sin (x)) :

True for all

x \in R

All critical points are in domain

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

What is the critical f(x)=ln(2+sin(x)) ?
The critical f(x)=ln(2+sin(x)) is x= pi/2+2pin,x=(3pi)/2+2pin