What is the critical f(x)=|sin(x)|,0<= x<= 2pi ?

The critical f(x)=|sin(x)|,0<= x<= 2pi is x=0,x=pi+2pin,x=2pi

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critical f(x)=|sin(x)|,0<= x<= 2pi

critical points

f (x) = ∣ sin (x) ∣, 0 \leq x \leq 2 π

x = 0, x = π + 2 πn, x = 2 π

Solution steps

∣ sin (x) ∣, 0 \leq x \leq 2 π

Absolute value functions are piecewise functions

Find the function intervals:

2 πn < x < π + 2 πn, x = π + 2 πn, π + 2 πn < x < 2 π + 2 πn

Join with the function interval:

2 πn < x < π + 2 πn, x = π + 2 πn, π + 2 πn < x < 2 π + 2 πn

Evaluate the function behavior for each interval

Find where

f^{'} (x)

is equal to zero or undefined

x = π + 2 πn

Evaluate interval endpoint

x = 0 :

critical point

Evaluate interval endpoint

x = 2 π :

critical point

x = 0, x = π + 2 πn, x = 2 π

What is the critical f(x)=|sin(x)|,0<= x<= 2pi ?
The critical f(x)=|sin(x)|,0<= x<= 2pi is x=0,x=pi+2pin,x=2pi