What is the critical f(x)=cos((2pi)/3 x) ?

The critical f(x)=cos((2pi)/3 x) is x=3n,x= 3/2+3n

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critical f(x)=cos((2pi)/3 x)

critical points

f (x) = cos (\frac{2 π}{3} x)

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

Solution steps

cos (\frac{2 π}{3} x)

Find where

f^{'} (x)

is equal to zero or undefined

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

Identify critical points not in

f (x)

domain

Domain of

cos (\frac{2 π}{3} x) : - \infty < x < \infty

All critical points are in domain

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

f (x) = 12 x^{5} + 30 x^{4} - 160 x^{3} + 7

f (x) = - 3 x^{4} + 20 x^{3} - 17

f (x) = 3 x^{2} - 12 x + 12

f (x) = - 3 x^{4} - 24 x^{2} + 4 y^{3} - 12 y - 20

f (y) = 5 (9650 - y^{2}) - 19 y

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