en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=2x-4cos(x)

Solution

extreme points

f (x) = 2 x - 4 cos (x)

Solution

Maximum (\frac{7 π}{6} + 2 πn, 2 (\frac{7 π}{6} + 2 πn) - 4 cos (\frac{7 π}{6} + 2 πn)), Minimum (\frac{11 π}{6} + 2 πn, 2 (\frac{11 π}{6} + 2 πn) - 4 cos (\frac{11 π}{6} + 2 πn))

Solution steps

Find the critical points:

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

Domain of

2 x - 4 cos (x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn \leq x < \frac{7 π}{6} + 2 πn,

Decreasing

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

Increasing

: \frac{11 π}{6} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{7 π}{6} + 2 πn

into

2 x - 4 cos (x) \Rightarrow y = 2 (\frac{7 π}{6} + 2 πn) - 4 cos (\frac{7 π}{6} + 2 πn)

Maximum (\frac{7 π}{6} + 2 πn, 2 (\frac{7 π}{6} + 2 πn) - 4 cos (\frac{7 π}{6} + 2 πn))

Plug the extreme point

x = \frac{11 π}{6} + 2 πn

into

2 x - 4 cos (x) \Rightarrow y = 2 (\frac{11 π}{6} + 2 πn) - 4 cos (\frac{11 π}{6} + 2 πn)

Minimum (\frac{11 π}{6} + 2 πn, 2 (\frac{11 π}{6} + 2 πn) - 4 cos (\frac{11 π}{6} + 2 πn))

Maximum (\frac{7 π}{6} + 2 πn, 2 (\frac{7 π}{6} + 2 πn) - 4 cos (\frac{7 π}{6} + 2 πn)), Minimum (\frac{11 π}{6} + 2 πn, 2 (\frac{11 π}{6} + 2 πn) - 4 cos (\frac{11 π}{6} + 2 πn))

Popular Examples

extreme f(x)=16xy-x^3-8y^2 extreme points

f (x) = 16 x y - x^{3} - 8 y^{2}

extreme f(x)=x+9/x+3 extreme points

f (x) = x + \frac{9}{x} + 3

extreme f(x)=-x^4+8x^2+10 extreme points

f (x) = - x^{4} + 8 x^{2} + 10

extreme f(x)=(x^{5/2-1}*e^{-x/2})extreme points

f (x) = (x^{\frac{5}{2} - 1} \cdot e^{- \frac{x}{2}})

extreme f(x,y)=sqrt(36-4x^2-9y^2)extreme points

f (x, y) = 36 - 4 x^{2} - 9 y^{2}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=2x-4cos(x) ?
The extreme f(x)=2x-4cos(x) is