What is the critical f(x)=2sec(x)+tan(x) ?

The critical f(x)=2sec(x)+tan(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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critical f(x)=2sec(x)+tan(x)

critical points

f (x) = 2 sec (x) + tan (x)

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

Solution steps

2 sec (x) + tan (x)

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Identify critical points not in

f (x)

domain

Domain of

2 sec (x) + tan (x) : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

2 sec (x) + tan (x)

is not defined at

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

, therefore:

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

What is the critical f(x)=2sec(x)+tan(x) ?
The critical f(x)=2sec(x)+tan(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin