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))

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

extreme

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))

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))