What is the extreme f(x)=-3/2 sin(3/2 x) ?

The extreme f(x)=-3/2 sin(3/2 x) is Minimum(pi/3+(4pi)/3 n,-3/2),Maximum(pi+(4pi)/3 n, 3/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=-3/2 sin(3/2 x)

extreme points

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

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

Solution steps

Find the critical points:

x = \frac{π}{3} + \frac{4 π}{3} n, x = π + \frac{4 π}{3} n

Domain of

- \frac{3}{2} sin (\frac{3}{2} x) : - \infty < x < \infty

Find intervals:

Decreasing

: \frac{4 π}{3} n \leq x < \frac{π}{3} + \frac{4 π}{3} n,

Increasing

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

Decreasing

: π + \frac{4 π}{3} n < x < \frac{4 π}{3} + \frac{4 π}{3} n

Plug the extreme point

x = \frac{π}{3} + \frac{4 π}{3} n

into

- \frac{3}{2} sin (\frac{3}{2} x) \Rightarrow y = - \frac{3}{2}

Minimum (\frac{π}{3} + \frac{4 π}{3} n, - \frac{3}{2})

Plug the extreme point

x = π + \frac{4 π}{3} n

into

- \frac{3}{2} sin (\frac{3}{2} x) \Rightarrow y = \frac{3}{2}

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

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

- x^{2} + 2

- x^{2} + 1

f (x) = 40 - 40 e^{- x}

f (x) = x (22 - 2 x) (\frac{37}{2} - x)

f (x) = \frac{4 e ^{- 2 x}}{2 x + 5}

What is the extreme f(x)=-3/2 sin(3/2 x) ?
The extreme f(x)=-3/2 sin(3/2 x) is Minimum(pi/3+(4pi)/3 n,-3/2),Maximum(pi+(4pi)/3 n, 3/2)