What is the critical |sin(x)| ?

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

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critical |sin(x)|

critical points

∣ sin (x) ∣

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

Solution steps

∣ sin (x) ∣

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

Evaluate the function behavior for each interval

Find where

f^{'} (x)

is equal to zero or undefined

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

f (x) = x^{4} - 8 x + 10

f (x) = \frac{6}{x + 2}

f (x) = 3 x^{2} - 4 x + 5

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 1

f (x, y) = x^{3} + x y + y^{2}

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