What is the extreme f(x)=x^2log_{10}(x) ?

The extreme f(x)=x^2log_{10}(x) is Minimum(1/(sqrt(e)),-1/(2e)log_{10}(e))

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extreme f(x)=x^2log_{10}(x)

extreme points

f (x) = x^{2} lo g_{10} (x)

Minimum (\frac{1}{e}, - \frac{1}{2 e} lo g_{10} (e))

Solution steps

f^{'} (x) = \frac{x + 2 x ln ( x )}{ln ( 10 )}

Find intervals:

Decreasing

: 0 < x < \frac{1}{e},

Increasing

: \frac{1}{e} < x < \infty

Plug

x = \frac{1}{e}

into

x^{2} lo g_{10} (x) : - \frac{1}{2 e} lo g_{10} (e)

Minimum (\frac{1}{e}, - \frac{1}{2 e} lo g_{10} (e))

f (x, y) = - x^{4} + 4 (x^{2} - y^{2}) - 3

f (x, y) = \frac{- x - ln ( x ^{2} + y ^{2} - 81 )}{666}

f (x) = sin (2 x) - x, - \frac{π}{2} \leq x \leq \frac{π}{2}

f (x) = 5 x^{4} - x^{5} + 8

f (x) = 5 x^{4} - x^{5} + 7

What is the extreme f(x)=x^2log_{10}(x) ?
The extreme f(x)=x^2log_{10}(x) is Minimum(1/(sqrt(e)),-1/(2e)log_{10}(e))