What is the extreme 3+sin(x) ?

The extreme 3+sin(x) is Maximum(pi/2+2pin,4),Minimum((3pi)/2+2pin,2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme 3+sin(x)

extreme points

3 + sin (x)

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

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Increasing

: 2 πn \leq x < \frac{π}{2} + 2 πn,

Decreasing

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

Increasing

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

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

3 + sin (x) \Rightarrow y = 4

Maximum (\frac{π}{2} + 2 πn, 4)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

3 + sin (x) \Rightarrow y = 2

Minimum (\frac{3 π}{2} + 2 πn, 2)

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

f (x, y) = e^{x} (x + y^{2} + 2 y)

f (x, y) = 3 y^{2} + 5 x y + y + x^{2} + 4 x - 5

9

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

f (x) = \frac{6 x}{x ^{2} + 25}

What is the extreme 3+sin(x) ?
The extreme 3+sin(x) is Maximum(pi/2+2pin,4),Minimum((3pi)/2+2pin,2)