What is the extreme f(x)=cos(pix),0<= x<= 1/6 ?

The extreme f(x)=cos(pix),0<= x<= 1/6 is Maximum(0,1),Minimum(1/6 ,(sqrt(3))/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=cos(pix),0<= x<= 1/6

extreme

Maximum (0, 1), Minimum (\frac{1}{6}, \frac{3}{2})

Solution steps

Find the critical points:

x = 0, x = \frac{1}{6}

Domain of

cos (π x), 0 \leq x \leq \frac{1}{6} : 0 \leq x \leq \frac{1}{6}

Find intervals:

Decreasing

: 0 < x < \frac{1}{6}

Plug the extreme point

x = 0

into

cos (π x) \Rightarrow y = 1

Maximum (0, 1)

Plug the extreme point

x = \frac{1}{6}

into

cos (π x) \Rightarrow y = \frac{3}{2}

Minimum (\frac{1}{6}, \frac{3}{2})

Maximum (0, 1), Minimum (\frac{1}{6}, \frac{3}{2})

What is the extreme f(x)=cos(pix),0<= x<= 1/6 ?
The extreme f(x)=cos(pix),0<= x<= 1/6 is Maximum(0,1),Minimum(1/6 ,(sqrt(3))/2)