What is the extreme f(x)=-3x+ln(x),(0,3) ?

The extreme f(x)=-3x+ln(x),(0,3) is Maximum(1/3 ,-1-ln(3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=-3x+ln(x),(0,3)

extreme points

f (x) = - 3 x + ln (x), (0, 3)

Maximum (\frac{1}{3}, - 1 - ln (3))

Solution steps

Find the critical points:

x = \frac{1}{3}

Domain of

- 3 x + ln (x), (0, 3) : 0 < x < 3

Find intervals:

Increasing

: 0 < x < \frac{1}{3},

Decreasing

: \frac{1}{3} < x < 3

Plug the extreme point

x = \frac{1}{3}

into

- 3 x + ln (x) \Rightarrow y = - 1 - ln (3)

Maximum (\frac{1}{3}, - 1 - ln (3))

x y + \frac{50}{x} + \frac{20}{y}

\frac{x}{x ^{3} + x ^{2} + 9}

f (x) = x^{4} - 128 x^{2} + 5

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

\frac{2 x}{x ^{2} + x - 20} \frac{3 x}{x ^{2} + 4 x - 5}

What is the extreme f(x)=-3x+ln(x),(0,3) ?
The extreme f(x)=-3x+ln(x),(0,3) is Maximum(1/3 ,-1-ln(3))