What is the extreme f(x)=sin^2(13x) ?

The extreme f(x)=sin^2(13x) is Minimum(pi/(13)n,0),Maximum(pi/(26)+pi/(13)n,1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=sin^2(13x)

extreme points

f (x) = sin^{2} (13 x)

Minimum (\frac{π}{13} n, 0), Maximum (\frac{π}{26} + \frac{π}{13} n, 1)

Solution steps

Find the critical points:

x = \frac{π}{13} n, x = \frac{π}{26} + \frac{π}{13} n

Domain of

sin^{2} (13 x) : - \infty < x < \infty

Find intervals:

Increasing

: \frac{π}{13} n < x < \frac{π}{26} + \frac{π}{13} n,

Decreasing

: \frac{π}{26} + \frac{π}{13} n < x < \frac{π}{13} + \frac{π}{13} n

Plug the extreme point

x = \frac{π}{13} n

into

sin^{2} (13 x) \Rightarrow y = 0

Minimum (\frac{π}{13} n, 0)

Plug the extreme point

x = \frac{π}{26} + \frac{π}{13} n

into

sin^{2} (13 x) \Rightarrow y = 1

Maximum (\frac{π}{26} + \frac{π}{13} n, 1)

Minimum (\frac{π}{13} n, 0), Maximum (\frac{π}{26} + \frac{π}{13} n, 1)

f (x) = x^{2} - 81

f (x) = \frac{7 x}{6 + x}

3 - e^{x}

(5, 4), (1, - 2)

\frac{1}{2 - 3 x}

What is the extreme f(x)=sin^2(13x) ?
The extreme f(x)=sin^2(13x) is Minimum(pi/(13)n,0),Maximum(pi/(26)+pi/(13)n,1)