What is the critical 2cos(x)-sin(2x) ?

The critical 2cos(x)-sin(2x) is x= pi/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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critical 2cos(x)-sin(2x)

critical points

2 cos (x) - sin (2 x)

x = \frac{π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

2 cos (x) - sin (2 x)

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Identify critical points not in

f (x)

domain

Domain of

2 cos (x) - sin (2 x) : - \infty < x < \infty

All critical points are in domain

x = \frac{π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

(- 4, 1), (2, - 3)

\frac{1}{x} + 3

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

y = - 1

f (x) = \frac{1}{3} x^{3} - x^{2} + x + 5

What is the critical 2cos(x)-sin(2x) ?
The critical 2cos(x)-sin(2x) is x= pi/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin