What is the extreme f(x)=2csc(x) ?

The extreme f(x)=2csc(x) is Minimum(pi/2+2pin,2),Maximum((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 f(x)=2csc(x)

extreme points

f (x) = 2 csc (x)

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

2 csc (x) : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Find intervals:

Decreasing

: 2 πn < x < \frac{π}{2} + 2 πn,

Increasing

: \frac{π}{2} + 2 πn < x < π + 2 πn,

Increasing

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

Decreasing

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

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

2 csc (x) \Rightarrow y = 2

Minimum (\frac{π}{2} + 2 πn, 2)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

2 csc (x) \Rightarrow y = - 2

Maximum (\frac{3 π}{2} + 2 πn, - 2)

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

f (x) = (x^{2} - 36)^{\frac{1}{11}}, - 7 \leq x \leq 6

x^{\frac{1}{5}} (x^{2} - 4)

f (x) = cos (\frac{4 x}{3})

\frac{5 x}{1 - x}

K (r, s) = 3 r - 7 s

What is the extreme f(x)=2csc(x) ?
The extreme f(x)=2csc(x) is Minimum(pi/2+2pin,2),Maximum((3pi)/2+2pin,-2)