What is the critical f(x)=6sec(x)+3tan(x) ?

The critical f(x)=6sec(x)+3tan(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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critical f(x)=6sec(x)+3tan(x)

critical points

f (x) = 6 sec (x) + 3 tan (x)

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

Solution steps

6 sec (x) + 3 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

6 sec (x) + 3 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

6 sec (x) + 3 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

f (x, y) = x + 8 y + \frac{1}{x y}

f (x, y) = - x^{2} + y^{2} + 2 x + 4 y + 7

\frac{x ^{2} + 3}{x - 1}

∣ x ∣ + \frac{x}{8}

f (x) = (x^{2} - y^{2}) (x^{2} + y^{2})

What is the critical f(x)=6sec(x)+3tan(x) ?
The critical f(x)=6sec(x)+3tan(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin