What is the extreme f(x)=x^2log_{7}(x) ?

The extreme f(x)=x^2log_{7}(x) is Minimum(1/(sqrt(e)),-1/(2e)log_{7}(e))

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extreme f(x)=x^2log_{7}(x)

extreme points

f (x) = x^{2} lo g_{7} (x)

Minimum (\frac{1}{e}, - \frac{1}{2 e} lo g_{7} (e))

Solution steps

f^{'} (x) = \frac{x + 2 x ln ( x )}{ln ( 7 )}

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{1}{e}

into

x^{2} lo g_{7} (x) : - \frac{1}{2 e} lo g_{7} (e)

Minimum (\frac{1}{e}, - \frac{1}{2 e} lo g_{7} (e))

U (x, y) = - x^{2} + 8 - y^{2}

f (x) = 2 x^{4} + 8 x^{2} - 8 x^{3} - 1

f (x) = 9 x^{3} - 54 x^{2} + 81 x + 13, (- 6, 2)

f (x) = x^{3} - 12 x^{2} + 45 x + 7

f (x) = x^{7} (x + 4)^{4}, - 10 \leq x \leq 13

What is the extreme f(x)=x^2log_{7}(x) ?
The extreme f(x)=x^2log_{7}(x) is Minimum(1/(sqrt(e)),-1/(2e)log_{7}(e))