What is the critical e^{ln(x)+1}-5cos(3x) ?

The critical e^{ln(x)+1}-5cos(3x) is x= pi/3+(arcsin(e/(15)))/3+(2pin)/3

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critical e^{ln(x)+1}-5cos(3x)

critical points

e^{l n (x) + 1} - 5 cos (3 x)

x = \frac{π}{3} + \frac{arcsin ( \frac{e}{15} )}{3} + \frac{2 πn}{3}

Solution steps

e^{l n (x) + 1} - 5 cos (3 x)

Find where

f^{'} (x)

is equal to zero or undefined

x = - \frac{arcsin ( \frac{e}{15} )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} + \frac{arcsin ( \frac{e}{15} )}{3} + \frac{2 πn}{3}

Identify critical points not in

f (x)

domain

Domain of

e^{l n (x) + 1} - 5 cos (3 x) : x > 0

e^{l n (x) + 1} - 5 cos (3 x)

is not defined at

x = - \frac{arcsin ( \frac{e}{15} )}{3} + \frac{2 πn}{3}

, therefore:

x = \frac{π}{3} + \frac{arcsin ( \frac{e}{15} )}{3} + \frac{2 πn}{3}

f (x) = \frac{ln ( x )}{ln ( 3 )}

f (x) = \frac{x}{x ^{2} - 4 x - 12}

\frac{2 x}{x - 5}

f (x) = 6 x^{2} - 6 x

2 x + 5 y = 10

What is the critical e^{ln(x)+1}-5cos(3x) ?
The critical e^{ln(x)+1}-5cos(3x) is x= pi/3+(arcsin(e/(15)))/3+(2pin)/3