What is the extreme g(θ)=5θ-9sin(θ) ?

The extreme g(θ)=5θ-9sin(θ) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme g(θ)=5θ-9sin(θ)

extreme points

g (θ) = 5 θ - 9 sin (θ)

Minimum (arccos (\frac{5}{9}) + 2 πn, 5 (arccos (\frac{5}{9}) + 2 πn) - 9 sin (arccos (\frac{5}{9}) + 2 πn)), Maximum (2 π - arccos (\frac{5}{9}) + 2 πn, 5 (2 π - arccos (\frac{5}{9}) + 2 πn) - 9 sin (2 π - arccos (\frac{5}{9}) + 2 πn))

Solution steps

Find the critical points:

θ = arccos (\frac{5}{9}) + 2 πn, θ = 2 π - arccos (\frac{5}{9}) + 2 πn

Domain of

5 θ - 9 sin (θ) : - \infty < θ < \infty

Find intervals:

Decreasing

: 2 πn \leq θ < arccos (\frac{5}{9}) + 2 πn,

Increasing

: arccos (\frac{5}{9}) + 2 πn < θ < 2 π - arccos (\frac{5}{9}) + 2 πn,

Decreasing

: 2 π - arccos (\frac{5}{9}) + 2 πn < θ < 2 π + 2 πn

Plug the extreme point

x = arccos (\frac{5}{9}) + 2 πn

into

5 θ - 9 sin (θ) \Rightarrow y = 5 (arccos (\frac{5}{9}) + 2 πn) - 9 sin (arccos (\frac{5}{9}) + 2 πn)

Minimum (arccos (\frac{5}{9}) + 2 πn, 5 (arccos (\frac{5}{9}) + 2 πn) - 9 sin (arccos (\frac{5}{9}) + 2 πn))

Plug the extreme point

x = 2 π - arccos (\frac{5}{9}) + 2 πn

into

5 θ - 9 sin (θ) \Rightarrow y = 5 (2 π - arccos (\frac{5}{9}) + 2 πn) - 9 sin (2 π - arccos (\frac{5}{9}) + 2 πn)

Maximum (2 π - arccos (\frac{5}{9}) + 2 πn, 5 (2 π - arccos (\frac{5}{9}) + 2 πn) - 9 sin (2 π - arccos (\frac{5}{9}) + 2 πn))

Minimum (arccos (\frac{5}{9}) + 2 πn, 5 (arccos (\frac{5}{9}) + 2 πn) - 9 sin (arccos (\frac{5}{9}) + 2 πn)), Maximum (2 π - arccos (\frac{5}{9}) + 2 πn, 5 (2 π - arccos (\frac{5}{9}) + 2 πn) - 9 sin (2 π - arccos (\frac{5}{9}) + 2 πn))

f (x) = 9 - x, (- 1, 3)

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

x^{3} + y^{3} - 2 x y

f (x, y) = x^{3} + y^{3} + 6 x^{2} - 9 y^{2} - 4

f (x) = \frac{1}{9} (x^{4} - 4 x^{3})