What is the extreme f(x)=x-ln(x), 1/2 <= x<= 2 ?

The extreme f(x)=x-ln(x), 1/2 <= x<= 2 is Maximum(1/2 , 1/2+ln(2)),Minimum(1,1),Maximum(2,2-ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x-ln(x), 1/2 <= x<= 2

extreme points

f (x) = x - ln (x), \frac{1}{2} \leq x \leq 2

Maximum (\frac{1}{2}, \frac{1}{2} + ln (2)), Minimum (1, 1), Maximum (2, 2 - ln (2))

Solution steps

Find the critical points:

x = \frac{1}{2}, x = 1, x = 2

Domain of

x - ln (x), \frac{1}{2} \leq x \leq 2 : \frac{1}{2} \leq x \leq 2

Find intervals:

Decreasing

: \frac{1}{2} < x < 1,

Increasing

: 1 < x < 2

Plug the extreme point

x = \frac{1}{2}

into

x - ln (x) \Rightarrow y = \frac{1}{2} + ln (2)

Maximum (\frac{1}{2}, \frac{1}{2} + ln (2))

Plug the extreme point

x = 1

into

x - ln (x) \Rightarrow y = 1

Minimum (1, 1)

Plug the extreme point

x = 2

into

x - ln (x) \Rightarrow y = 2 - ln (2)

Maximum (2, 2 - ln (2))

Maximum (\frac{1}{2}, \frac{1}{2} + ln (2)), Minimum (1, 1), Maximum (2, 2 - ln (2))

f (x, y) = 9 x^{2} + 18 x y + y^{3}

f (x) = 2 x^{2} + 3 x - 5

f (x) = x^{3} - 12 x - 10

g (x) = x^{2} - 6 x - 12

f (x) = - 6 x + 5 y

What is the extreme f(x)=x-ln(x), 1/2 <= x<= 2 ?
The extreme f(x)=x-ln(x), 1/2 <= x<= 2 is Maximum(1/2 , 1/2+ln(2)),Minimum(1,1),Maximum(2,2-ln(2))