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Popular >

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

Solution

extreme points

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

Solution

Maximum (\frac{2 π}{3} + 2 πn, \frac{2 π}{3} + 2 πn + 2 sin (\frac{2 π}{3} + 2 πn)), Minimum (\frac{4 π}{3} + 2 πn, \frac{4 π}{3} + 2 πn + 2 sin (\frac{4 π}{3} + 2 πn))

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Increasing

: 2 πn \leq x < \frac{2 π}{3} + 2 πn,

Decreasing

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

Increasing

: \frac{4 π}{3} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{2 π}{3} + 2 πn

into

x + 2 sin (x) \Rightarrow y = \frac{2 π}{3} + 2 πn + 2 sin (\frac{2 π}{3} + 2 πn)

Maximum (\frac{2 π}{3} + 2 πn, \frac{2 π}{3} + 2 πn + 2 sin (\frac{2 π}{3} + 2 πn))

Plug the extreme point

x = \frac{4 π}{3} + 2 πn

into

x + 2 sin (x) \Rightarrow y = \frac{4 π}{3} + 2 πn + 2 sin (\frac{4 π}{3} + 2 πn)

Minimum (\frac{4 π}{3} + 2 πn, \frac{4 π}{3} + 2 πn + 2 sin (\frac{4 π}{3} + 2 πn))

Maximum (\frac{2 π}{3} + 2 πn, \frac{2 π}{3} + 2 πn + 2 sin (\frac{2 π}{3} + 2 πn)), Minimum (\frac{4 π}{3} + 2 πn, \frac{4 π}{3} + 2 πn + 2 sin (\frac{4 π}{3} + 2 πn))

Popular Examples

range of f(x)=5+sqrt(4-x)range

f (x) = 5 + 4 - x

range of \sqrt[3]{x}+1 range

inverse of f(x)=27x^3 inverse

f (x) = 27 x^{3}

domain of f(x)=sqrt(-5x^2+40x+45)domain

f (x) = - 5 x^{2} + 40 x + 45

intercepts of f(x)=x^2 intercepts

f (x) = x^{2}

Frequently Asked Questions (FAQ)

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