What is the extreme f(x)=-5x^7ln(2x),(0,6) ?

The extreme f(x)=-5x^7ln(2x),(0,6) is Maximum(1/(2\sqrt[7]{e)}, 5/(896e))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=-5x^7ln(2x),(0,6)

extreme

Maximum (\frac{1}{2 7 e}, \frac{5}{896 e})

Solution steps

Find the critical points:

x = \frac{1}{2 7 e}

Domain of

- 5 x^{7} ln (2 x), (0, 6) : 0 < x < 6

Find intervals:

Increasing

: 0 < x < \frac{1}{2 7 e},

Decreasing

: \frac{1}{2 7 e} < x < 6

Plug the extreme point

x = \frac{1}{2 7 e}

into

- 5 x^{7} ln (2 x) \Rightarrow y = \frac{5}{896 e}

Maximum (\frac{1}{2 7 e}, \frac{5}{896 e})

What is the extreme f(x)=-5x^7ln(2x),(0,6) ?
The extreme f(x)=-5x^7ln(2x),(0,6) is Maximum(1/(2\sqrt[7]{e)}, 5/(896e))