What is the extreme f(x)=3x^4-7ln(x) ?

The extreme f(x)=3x^4-7ln(x) is Minimum(\sqrt[4]{7/12}, 7/4-7/4 ln(7/12))

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extreme f(x)=3x^4-7ln(x)

extreme

Minimum (4 \frac{7}{12}, \frac{7}{4} - \frac{7}{4} ln (\frac{7}{12}))

Solution steps

f^{'} (x) = 12 x^{3} - \frac{7}{x}

Find intervals:

Decreasing

: 0 < x < 4 \frac{7}{12},

Increasing

: 4 \frac{7}{12} < x < \infty

Plug

x = 4 \frac{7}{12}

into

3 x^{4} - 7 ln (x) : \frac{7}{4} - \frac{7}{4} ln (\frac{7}{12})

Minimum (4 \frac{7}{12}, \frac{7}{4} - \frac{7}{4} ln (\frac{7}{12}))

What is the extreme f(x)=3x^4-7ln(x) ?
The extreme f(x)=3x^4-7ln(x) is Minimum(\sqrt[4]{7/12}, 7/4-7/4 ln(7/12))