What is the extreme f(x)=(x^6)/6-ln(x) ?

The extreme f(x)=(x^6)/6-ln(x) is Minimum(1, 1/6)

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extreme f(x)=(x^6)/6-ln(x)

extreme

Minimum (1, \frac{1}{6})

Solution steps

Find the critical points:

x = 1

Domain of

\frac{x ^{6}}{6} - ln (x) : x > 0

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

\frac{x ^{6}}{6} - ln (x) \Rightarrow y = \frac{1}{6}

Minimum (1, \frac{1}{6})

What is the extreme f(x)=(x^6)/6-ln(x) ?
The extreme f(x)=(x^6)/6-ln(x) is Minimum(1, 1/6)