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

The extreme f(x)=x^6+x/6 is Minimum(-1/(\sqrt[5]{36)},-5/(36\sqrt[5]{36)})

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extreme f(x)=x^6+x/6

extreme

Minimum (- \frac{1}{5 36}, - \frac{5}{36 5 36})

Solution steps

f^{'} (x) = 6 x^{5} + \frac{1}{6}

Find intervals:

Decreasing

: - \infty < x < - 5 \frac{1}{36},

Increasing

: - 5 \frac{1}{36} < x < \infty

Plug

x = - \frac{1}{5 36}

into

x^{6} + \frac{x}{6} : - \frac{5}{36 5 36}

Minimum (- \frac{1}{5 36}, - \frac{5}{36 5 36})

What is the extreme f(x)=x^6+x/6 ?
The extreme f(x)=x^6+x/6 is Minimum(-1/(\sqrt[5]{36)},-5/(36\sqrt[5]{36)})