What is the critical f(x)=sin(4x) ?

The critical f(x)=sin(4x) is x= pi/8+pi/2 n,x=(3pi)/8+pi/2 n

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critical f(x)=sin(4x)

critical points

f (x) = sin (4 x)

x = \frac{π}{8} + \frac{π}{2} n, x = \frac{3 π}{8} + \frac{π}{2} n

Solution steps

sin (4 x)

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{π}{8} + \frac{π}{2} n, x = \frac{3 π}{8} + \frac{π}{2} n

Identify critical points not in

f (x)

domain

Domain of

sin (4 x) : - \infty < x < \infty

All critical points are in domain

x = \frac{π}{8} + \frac{π}{2} n, x = \frac{3 π}{8} + \frac{π}{2} n

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

f (x) = 4 x - 7

f (x) = \frac{1}{x - 9}

y = \frac{2}{3} x - 2

What is the critical f(x)=sin(4x) ?
The critical f(x)=sin(4x) is x= pi/8+pi/2 n,x=(3pi)/8+pi/2 n