What is the extreme f(x)=x-ln(x),0<= x<= 2 ?

The extreme f(x)=x-ln(x),0<= x<= 2 is 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),0<= x<= 2

extreme points

f (x) = x - ln (x), 0 \leq x \leq 2

Minimum (1, 1), Maximum (2, 2 - ln (2))

Solution steps

Find the critical points:

x = 1, x = 2

Domain of

x - ln (x), 0 \leq x \leq 2 : 0 < x \leq 2

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 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))

Minimum (1, 1), Maximum (2, 2 - ln (2))

f (x) = x^{3} - 24 ln (x) + 5

f (x) = 16 x + 19 x^{\frac{16}{19}}

f (t) = t^{2} + \frac{1}{t}

y = \frac{1}{3} x^{3} + 2 x^{2} + 3 x

f (x) = y \cdot (e^{x} - 1)

What is the extreme f(x)=x-ln(x),0<= x<= 2 ?
The extreme f(x)=x-ln(x),0<= x<= 2 is Minimum(1,1),Maximum(2,2-ln(2))