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

The critical f(x)=x+2sin(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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critical f(x)=x+2sin(x)

critical points

f (x) = x + 2 sin (x)

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

x + 2 sin (x)

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Identify critical points not in

f (x)

domain

Domain of

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

All critical points are in domain

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

f (x) = 4 x^{2} (5^{x})

f (x) = x^{3} - 3 x^{2} + 8

(6, 5), (2, 0)

f (x) = 2 x^{4} - 8 x^{3}

f (x) = - 5 x^{2} + 40 x

What is the critical f(x)=x+2sin(x) ?
The critical f(x)=x+2sin(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin